Speech Transcript - What Is Light And How Does It Interact With Matter? - Lectures on photon emission and absorption

let's talk about electromagnetic radiation

electromagnetic radiation

is the wave like property

it has alternating magnetic and electric fields

now we're not gonna talk about the electric and magnetic fields too much but the

wave nature is important to us what are the properties of ways

well while family with waves event at the beach we've seen waves come in from

the ocean

one of the properties

well there's a speed of the wave moves

if you see a search for any catches the wave

the speed that the server moves writing the class pressed

is the speed of the way

we write that down

in on the board as a sine wave

that will designate our wave like property and if it travels

in the

certain direction will give that direction of travel

and we'll give it is seen

when we talk about electromagnetic radiation

it moves at the speed of light

as opposed to the speed of server

so this mean is the speed of light

what other properties the waves have

well there's quality the separation between the crest of the way

if you see one server catch a wave and another server catch the wave right

behind him

the separation between those two surfers

as they approach the beach is the wave like

and their speed will be equal and their distance will stay about the same

their distance between and the wavelength

the length between the crest

is given the symbol lander and is the wavelength of the way

an example seven hundred an animator wave like

that wavelength corresponds to a wavelength in the visible region of the electromagnetic spectrum visible

light

and often use the term light and electromagnetic radiation interchangeably

seven hundred nanometres when that wreck electromagnetic radiation strikes are i appears reddish

electromagnetic radiation with wavelength four hundred nanometres appears polish

so the different wavelengths have different properties

and for some electromagnetic radiation are sensitive to them

we have different colours for different wavelengths

another property of ways are the frequency

the frequency the way it is how often a wave crest past you

so you have

three wave crests past you per second

the frequency would be one over three or one third of the second

now we say reciprocal seconds one over three seconds we give that

a special unit called hz

one third of our hz

one over three seconds

the way blank the frequency

always multiplied together to giving the speed

product of the wavelength in the frequency is the speed

and for electromagnetic radiation that's the speed of light

three times ten to the eight meters per second

we're gonna talk about weight is electromagnetic radiation and light

all the time in discourse so we should be very familiar with the relationships between

electromagnetic radiation frequency wavelength and speed

electromagnetic radiation encompasses a broader range of wave like some frequencies

from

astronomical proportions ten to the eight meters like

for the sun distances

down to

tiny microscopic

with like stand of the minus sixty meters

the range is have different names basically historical

names

describing the kinds of radiation in each band

the long wavelengths radio waves

microwave slightly shorter in wavelength still though

in proportions we could

resolve

few meters to a few centimetres

infrared radiation now down below are

range of resolving it

and visible ultraviolet radiation

x rays and gamma rays

all these flavours of radiation are emitted by the sign so during solar of ends

the proof is bayes by all these kinds of radiation and there's other sources of

these radiation obviously we can make microwaves in radio waves

infrared waves and visible ways we have flashlight with microwave ovens we have meters we

have radios

so all those things are were able to

produce electromagnetic radiation

the visible spectrum in particular in between the infrared and ultraviolet we're gonna look at

a lot

these are the wavelength that our allies are sensitive to

from four hundred to seven hundred ninety meters approximately

so blue green yellow or orange and red light

we can detect

and these wavelengths stimulate a rise and those signals travel to our brain we perceive

different colours

the combination of all those colours

altogether would give us a white light

from blue to read

completely all at once

you would perceive white light

but you can take one light and break it back down into its component colours

you can do that with

putting obstacles in the way putting a grading in the way of the light

so the light

of different way likes interact differently with that grading or those obstacles so long waves

wave like sort of reacted differently than short wavelengths

you can spread out

the wavelength in space

we can actually do that diffraction grating tsar cheap and easy to make

there's actually some in these classes here

what i'm gonna do is undertake this white light source

i'm gonna turn that on and we'll put on these the fraction glasses and will

be able to see when we look at the light

it resolved into

blue green

orange red it's component colours

so this is a beautiful example of the electromagnetic spectrum

white light being resolved into its component wavelength

by a diffraction grating

we talking a lot about

wavelengths

and visible light during the scores

so this experiment with the diffraction grating showing separation of wavelengths

is very useful for understanding of light

when you talk about electromagnetic waves the waves are properties of an electric and magnetic

field

and they're

they can be very long like radio waves what i can be very short like

gamma waves

but

there's no sense that we have they can perceive then we can see them are

smell them are touch them or understand the wave behavior

when we look at ocean waves it's obvious that there is a wave property and

we can see their speed and they're

wavelength and their frequencies

well electromagnetic radiation you can't

so be nice to be able to demonstrate

the wave property in experiment

well with ocean waves waterways it's well known windows waves hit obstacles how they behave

it be need to arrange an experiment where electromagnetic wave hit some obstacles and display

those same kind of wave characteristics

so that's what we're gonna do

so consider this we're gonna take us let a tiny little hole poked in a

screen and shine light through it and then look far away

at a wall or some other screen without like it's and c with that looks

so i think you understand as you take this is like

poking a hole in a pie plate and shining a flashlight through it on will

wall

you know what you'd see you see

an image of the whole that you poked and it be diffuse around the edges

and it be bright in the centre

that's because the light is distracting in spreading out

around the edges of the a whole you pop

that's exactly what are drawn here i have a light passing through a

a whole

at a screen far away

and i've applied in the intensity distribution

now this is monochromatic lights only one wavelength involved it's not like a flashlight

so the more like a laser

going through a slit

what you have the always the same thing a bright spot beginning do at the

edges live pointed out here

so this intensity distribution is just like

a probability distribution if it were particles

that is

let's say i shot bullets or babies or something through a whole

some of them would take off the sides here in a spread out in a

and out of the fringes but a lot i will go right through

and hit directly across from the whole

so you'd have a high probability of by a particle hitting directly across from the

whole

and slightly lower probability as you move away from the whole

so let's look at another slit we could do the same thing with light

a second slip and have the same kind of experience

where a lot of particles are a lot of waves are a lot of beams

it directly across from the slit

so to sleep together is where gets interesting

when waves interact

that's how we can tell their way

and you probably know this by looking at waves in the bathtub or waves on

the beach

if there's something in the middle and waves hit them

there's a pattern

that's

predictable as those waves moves away from the article

so this is like an obstacle to

to light waves

and we'll talk about like in the visible spectrum so you can actually see it

so two slits

but like passes through them

what you might expect first as well you get a bright spot across from one

slit and a bright spot across from the other split

and it turns out for some wavelength in the first

orientation of this leads that's what you get

but if you range the slit appropriately

you get a very distinct patterns

instead of

two

strong intensities

across from slit a and slid be

what you actually see

eight

had and of intensities light and dark spots

the art

directly across from the slits

so you see bright spot

dark spot bright spot dark spot right but dark spot

alternating away from the center

of the slits the brightest spot is actually right between the slits

that doesn't look like a particle like property at all

particles would never do this if you change your b b's

or your

ping pong balls or something macroscopic to these two holes you would get a bright

spot here in a high probability spot here

so this is a property only of weights

and how can we understand it

well it's actually pretty clear

if you think about it always has to travel

from the slits

to the screen

and if the light has to travel from this leads to the screen so here's

a way of coming from each slit

in the centre

notice that the distance that this wave has to travel and the distance that wave

has to travel will be the same

so two waves travelling in units in the same distance

will be in phase

they will be either add up peak

or a trough

identically

because they've travelled the same distance

now what about it didn't spot up here

well if you think about a wave travelling from this little in a way of

travelling from this that ms wave now has a longer distance to travel

then this way

so the one that has the farther path is gonna be out of phase somewhat

with the one that has the shorter pat

so think about that one wave travels up down up down up the other one

has a longer path

up down up down up down

so what a rise in an phase the other arrives at the down phase

and when you add those two intensities together

what you get is destructive interference

so the waves added to give a zero intensity

it's actually really cool and it's something you can see in the experiments that will

show you later on we'll showing a laser through a slit

and will actually show you this pattern of light and dark spots

this shows us that electromagnetic radiation is actually a way

when the demo level slightly wary set up a laser to slip interference pattern

is set up a laser

a set of two closely spaced slides

in the screen where we can observe the alternating light and dark spots corresponding to

constructive and destructive interference

so let's think about this interference pattern of light in terms of a can quiz

so if you science a green light

and you

ten this

to slit interference pattern

how that interference pattern change if you increase the wavelength lander

so you go from say relayed to read like to longer wavelength light

how the interference pattern change will be better get more compact look about the same

or really get more dispersed

think about that per second and make a selection

let's consider three possible

explanation for the three answers may increase wavelet causes higher frequency spacing since wavelength and

frequency are inversely proportional

or be the interference depends only on the spacing between the slits

so increasing the wave like doesn't change anything and no change that occur

or c

longer wavelength white causes destructor interference a larger intervals

along the wall

think about those three options and make another selection

when you change the wavelength

in a to slit experiment what do you expect will happen

well

what we know from artist let wave interference pattern is

two slits "'cause" in a high intensity then low intensity because the

path are equal

right between the two slits

but if you go to the first peak say then one way as to travel

farther than the other

and it's that

extra distance

because is either constructive a bright spot or destructive a didn't spot

interference

on the screen

so but a larger

the wavelength

the larger the spacing will be

that is you have to move farther up the screen

to make this path like long enough to get it extra half wavelength

and give you

constructive or destructive interference up a screen

so longer wavelength means the spreading out

of the diffraction pattern

on the screen and the correct answer is c

so let's think about this interference pattern of light in terms of a can quiz

so if you shanks a green light

and you

ten this to slit interference pattern

how that interference pattern change if you increase the wavelength lander

so you go from say relayed to read like longer wavelength light

how the interference pattern change will be better get more compact will look about the

same or really get more dispersed

think about that per second and make a selection

let's consider three possible

explanation for the three answers may increase waveline causes higher frequency spacing since wavelength and

frequency are inversely proportional

or be the interference depends only on the spacing between the slits

so increasing the wave like doesn't change anything and no change whittaker

or c

longer wavelength white causes destructor interference a larger intervals

along the wall

think about those three options and make another selection

when you change the wavelength

and a to slit experiment what do you expect will happen

well

what we know from artist let wave interference pattern is

two slits "'cause" in a high intensity then low intensity because the

has are equal

right between the two slits

but if you go to the first peak say then one way as to travel

farther than the other

and it's that

extra distance

that causes either constructive a bright spot or destructive a didn't spot

interference

on the screen

so we larger

the wavelength

the larger the spacing will be

that is you have to move farther up the screen

to make this path blank long enough to get it extra half wavelength

and give you

constructive or destructive interference up a screen

so longer wavelength means the spreading out

of the diffraction pattern on the screen and the correct answer is c

when electromagnetic radiation interacts with matter that radiation can be changed or it can be

emitted

or it can be absorbed in some way

this is a really important phenomenon chemistry because we can see atoms and molecules with

a rise

in fact

when you see on t v a scientist

they'll always have

a lab coat to have some safety glasses

and

regardless what kind assigned just as being portrayed the always have a microscope

and when one to tell you something about an atom or molecule they look to

their microscope in a cell without will default you'll lose

that is just crazy

we can see there's no optical microscope they can result atoms and molecules

what we do is we have radiation of various wavelengths interact with atoms and molecules

and we'd dues things about the molecules based on how those atoms and molecules interact

with the radiation

so we're radiation it's a molecule or atom or any kind of matter

many things can happen it can be absorbed it

radiation can be admitted by excited atoms relation can change

from high frequency to low frequency radiation there can be a reflection process

all kinds of different things that help us understand the matter

so let's talk about absorption and emission

i can happen in many different ways

you can have a continuous absorption

so you can have

continuous absorption

of many wavelengths

so a band of wavelengths different colours hitting you all at once

so for instance when we see white light that's all the colours mixed together coming

at us

or we can see a book read

or yellowish orange several different wavelengths

coming out as it once

for several different wavelength could be

absorb at once

so absorption and emission

happen

in continuous broad swaths of radiation

and this is actually why you perceive colour

when white light a combination of all the colours it's an object

some of those colours can be absorbed

the colours that aren't absorb passed through

or reflected back and pitch your bibles

and the wavelength that hit your eyeballs can be either red or blue or re

for instance the screen looks blue because

wavelengths of white light are hitting it

but only the blues are coming back and hitting your mobile

now

absorption and emission can also be discrete or line base that is specific wavelengths are

absorbed

so you can broadcast

have a lot of radiation hitting an object in a broadband

but only sort in wavelengths are absorbed and removed from the spectrum

that's how that would look now you could also have that intonation you could have

only certain

wavelengths emitted from an excited atom or molecule are excited matter

again this would help you perceive colour of

a blue and r

green and the yellow

wavelength were emitted from an object

that object

would appear

greenish blue

so we can actually look at absorption and emission from atoms and i can show

you a continuous

emission spectrum it's actually

several lines being emitted at once

from atoms

so let's look at that

a but on my safety glasses so we can do an experiment safely if you're

on the desktop

and i'm gonna bring in

a series of tulips filled with

now there's various different gases here and i can excite these gases with an electric

current

and then they'll unit

electromagnetic radiation back to you in the visible region so you can see

a luxury son there aren't in the visible region

but we can see them so it doesn't matter

what i'm gonna do i'll take an electric

current here a little stimulator

and

stimulate these atoms of gas and you should see my visible radiation coming out of

the two

so there it is

she is a decision from side as

in the visible range

that's a really interesting experiment it shows

when a line spectrum is invaded

and there are several lines that ones

you'll see kind of a bluish green or a purplish colour

let's look at absorption

here i have some coloured solutions

and wireless solutions colour well white light is hitting them

and when the white light hits them

several wavelength are absorbed

all their wavelength passed directly through and he chewing the eyeball

so red wavelength

passed through a hit you in the eyeball for the solution and wu wavelengths

other colours absorb but who passes through

and hit you when the eyeball

so we're say

all colours but read are absorbed by this

can i prove that in a different way

well

here's a red pen laser

if i shine this red pen laser under my hand

i think it can see it there

now what i'm gonna do is i'm gonna shine this red pen laser through the

red solution

and i'm telling you and i think you probably agree with me that the red

should pass right through because this solution

does not absorb read

reds hitting your eyeballs now

so this red pen laser now passing through the solution

still hits my head

but i told you this blue solution it must be absorbing reds or you be

seen some rad

so i should be able to take my red pen laser

here it is just on my hand again

and passed through this blue solution

and have the red pen laser absorb so let's do that

here it is hitting just my hand and i'm gonna move back to like go

through the solution and you can see

the red is now absorbed by that blue solution

that's a beautiful demonstration of

a discrete

a single wavelength align absorption

by a blue solution

that's how colours work

absorption and emission we're gonna talk about a lot in discourse because they help us

understand matter

so let's think about this interference pattern of light in terms of a can quiz

so if you science a green light

and you

ten this

to slit interference pattern

how that interference pattern change if you increase the wavelength lambda

so you go from say relayed to read like longer wavelength light

how the interference pattern change

will be better get more compact will look about the same or really get more

dispersed

think about that per second and make a selection

let's consider three possible

explanation for the three answers may increase wavelet causes higher frequency spacing since wavelength and

frequency are inversely proportional

or be the interference depends only on the spacing between the slits

so increasing the wave like doesn't change anything and no change that occur

or c

longer wavelength white causes destructor interference a larger intervals

along the wall

think about those three options and make another selection

when you change the wavelength

in a to slit experiment what do you expect will happen

well

what we know from artist let wave interference pattern is

two slits "'cause" in a high intensity then low intensity because the

path are equal

right between the two slits

but if you go to the first peak say then one way as to travel

farther than the other

and it's that extra distance

because is either constructive a bright spot or destructive a didn't spot

interference

on the screen

so the larger

the wavelength

the larger the spacing will be

that is you have to move farther up the screen

to make this path like long enough to get it extra half wavelength

and give you

constructive or destructive interference up a screen

so longer wavelength means the spreading out

of the diffraction pattern on the screen and the correct answer is c

when the demo level slightly wary set up an experiment

to show absorb ins

coloured solutions is broken up the white light into its component colours and when you

place is a red solution in the past of the white light

notice that read it is transmitted

but green and blue are absorbed

now a yellow solution

when the yellow solution is placed in the path of the white light

we'll see that the blue is strongly absorbed

and the combination of red and green

is what causes the yellow colour

finally

we have a blue solution

the blue solution

should absorb

the red and the green and transmit the blue

so here we see the origin of colours

colours are absorbed and transmitted resulting in the colours that we observe thank you honey

so let's talk about absorption of light in terms of it can quiz

if you have an object that has an absorption spectrum that looks like this what

color is that object

is it blue green or red

think about that for a minute and make a selection

but continue argument for each of the possible answers

answer a blue light passes through the filters of the article your blue

answer be a filter that absorbs read and passes blue or making an object appeared

green

red line is absorbed by the filter so the object will appear red

think about those three possible solutions for a minute and make another selection

and object that has

and absorption spectrum that looks like this

is absorbing strongly in the reds and yellows

and passing

wavelength and the blue so we wavelengths will pass through

strike your i and this object

will appear blue

let's look at a couple filters and how they'll affect a blue object

so three possible filters

put in front of a blue object

which one of them

would make the object appear black

think about that for a minute

and make a selection

let's look at some possible explanations for each option

filter one the passes blue light and by the way

which combine to form black

or option be filter to absorb the blue light from the blue object making it

appear black or

filter three removes violet and ultraviolet light making the object appear black

think about those and make another selection

so we've got a little object

we're gonna put filters between the blue object and us and we're gonna see what

we see so

a blue object

wavelength the blue light

are being emitted from that object that's white appears blue

how do we make it appear black

we have to remove that remaining blue wavelengths

assumption removing all the wavelengths

from that object so non here are i and we have a black object

so we need to fine

a filter that absorbs strongly in the blue

and that is

filter number two

correct answer here

we all know glasses transparent

so let's look at absorption over a broader range of electromagnetic spectrum

transparent glass

should have an absorption spectrum that looks like either one or two or three

think about that for a minute and make a selection

let's look an argument for each of the answers

a transparent glass passes all visible wavelength

and only absorbed above the u b

or b

transparent glass must absorb some like in the visible region

or c transparent glass most absorb the entire visible region

think about those alternatives

and make another selection

if the option spectrum are transparent glass is what we're talking about

and we're talking about a rather broad region of electromagnetic spectrum from ultraviolet wavelengths down

to infrared wavelengths and i've

overlay the common visible coloured wavelengths

in the centre

so let's look at those three absorption spectra number one

absorb strongly in the ultraviolet

number to absorb strongly not the ultraviolet and

some visible wavelengths

an option three absorbs

ultraviolet visible wavelengths

looks like most of them and terminate somewhere in the i r so it also

absorbs a little bit of infrared

wavelengths as well but in order for the glass to be transparent

all visible wavelengths must pass through

transparent glass will pass white like directly through it you can see all colours to

transparent glass

so all colours must pass through

so we have to choose one that has

no absorption

spectra in the visible range that is option one

so the correct answer here

is k

but still calculation with electromagnetic radiation the properties of wavelet in frequency

what frequency and designation of radiation with wavelength eight point eight three p commuters

is emitted from technician

ninety nine during its nuclear decay

we understand a wavelength

a point eight three you can meters we can change that into a frequency

knowing that the way

waves travel at the speed of light c

so the product of the wavelength in the frequency

is the speed we can solve for the frequency

frequency is the speed over the wavelength

and just simply plug those two numbers in

a point eight three and now i've written ten to the minus twelve meters

because my

speed of light is

it has the units of meters per second so one all my units to be

the same

i can do that division three point four times ten to the nineteenth reciprocal seconds

three point o four three point four times ten to the nineteen her

so very high frequency very short wave like those we'd expect what

region of electromagnetic spectrum of that correspond to

well

this

wavelength in p commanders firmly in the gamma wave region of the spectrum so we

have

gavel waves emitted from technician ninety nine during its nuclear decay

but still calculation with electromagnetic radiation the properties of wavelength and frequency

what frequency and designation of radiation with wavelength eight point eight three p commuters

is emitted from technician

ninety nine during its nuclear decay

we understand a wavelength

eight point eight three p commuters we can change that into a frequency

knowing that the way

waves travel at the speed of light c

so the product of the wavelength in the frequency

is the speed we can solve for the frequency

frequency is the speed over the wavelength

and just simply plug those two numbers in

a point eight three and now i've written tend of the minus twelve meters

because my

speed of light is

it has the units of meters per second so one all my units to be

the same

i can do that division three point four times tend to the nineteenth reciprocal seconds

three point o four three point four times ten to the nineteen her

so very high frequency very short wave like those we'd expect what

region of electromagnetic spectrum of that correspond to

well

this

wavelength in p commanders firmly in the gamma wave region of the spectrum so we

have

gavel waves emitted from technician ninety nine during its nuclear decay

electromagnetic radiation is composed of wavelengths from very long the very short

we've talked about the relationship

between the wavelength the frequency and the speed of electromagnetic radiation

in fact the product go

wavelength and the frequency is the speed

for electromagnetic radiation light

speed is fixed at the speed of like

so you have the wavelength increases the frequency has to decrease their inversely proportional

and you can see i have

wave like increasing here and frequency increasing here

the visible region in particular we really talk a lot about because we can

perceive the length of the radiation by the colour

so we can make that easy connection between all wave

and it's blank by the colour that we see

long wavelength in the visible region

are read

intermediate wavelength going down from yellow to orange the green the blue

indigo and violet

from

long to shortwave links

in fact this kind of spells the guy's name role in g b are from

long to shortwave likes i often write that down and i can remember the colours

of the rainbow

now there's more properties to electromagnetic radiation in waves in general

for instance the intensity we haven't touched on that yet

you can think of the intensity of waves in the ocean as their height as

they come in

to the shore

a big way would be an intense way that all wave and intense way

i do we do that for electromagnetic radiation

well let's talk about intensity more as we go through this talk

now the intensity of light or electromagnetic radiation maybe more of an intuitive property that's

looking at this way

if you have and intensity originally of

i zero

you passing through a filter and you can and intensity of half that i zero

over two

well with the intensity mean if you put an additional column in the past

so i zero going through a

pair of identical filters

with that reduce the intensity down to acquire and or zero of the original intensity

think about that for a minute and make a selection

let's consider an argument for each of the possible answers

hey

a second filter reduces the intensity by one half again so you have a quarter

of the original intensity

be the second filter has twice the effect reducing the ten c by a factor

of four so one at the original or option c

the first filter removes half intensity so the second remove the remaining intensity giving you

zero intensity

think about those three possibilities and make a selection

so we've been talking about intensity the brightness of light

in terms of extenuating or reducing it with a filter

and original intensity reduced to half the brightness

by a single filter

what would be near fact

and identical filter put in the path again

well

if the first filter reduces it by

one half so it's half is bright here

a second filter would make this

half is bright

so you go from have the original intensity to a quarter of the original intensity

after two filters

so the correct answer here is a one quarter the original intensity

the intensity of light words brightness

can be considered in a thought experiment

just like we did with matter

we said

if i take a chunk of carbon

solid matter and i cut in half and then in half again and again and

again and continue cutting in and have to like get the tiniest piece of matter

it still has the properties of carbon

that timing is particle

would be an atom

can we do that with light intensity can we take a bright light

and bring in filters that reduce the intensity by a factor of two

cut the light intensity and have

again and again and again and again and again

well of course we can do the experiment

what happens

well if you're watching this experiment the light would get dimmer

as each filter was added

and they like what eventually didn't completely

but then something interesting would happen

you would see

individual

flashes of light

it turns out here eyes are accustomed to the smallest unit of like

individual pulses

these individual pulses like particles of like just like chopping matter up into you get

these smallest

particle an atom

you can reduce length intensity to you get the smallest particle of light

in we call these particles of light these tiny flashes we call them photons

and is four times carry the smallest amount of energy of light

time

is what we call it mean energy of the photon is given by h blocks

constant

times

the frequency of the light

so the frequency of a light times punks constant

gives you the energy of the photon one of the most important

equations in this class

in fact if you take nothing else open can one

take on the fact that the energy photons is given by

blanks constant times their frequency

once constant a very small number

six point six two times ten to the minus thirty fourth

jules seconds

that tells you this incredibly tiny amount of energy

but our eyes can detect that's the interesting thing

you do this experiment in a dark room where your eyes are acclimated to the

dark your pupils wide open

you can actually reduce intensity you see the individual flashes afford that

fascinating experiment to do

now visual perception has been quantitative for a long time

we've said that the limits of human perception are a candle

on a clear dark night at thirty miles away

that's when the intensity is at the level of individual photons hitting your i

light has a particle nature just like matter has a particle nature

now we can detect that particle nature

of electromagnetic radiation of all forms this we did a thought experiment on

visible light

we can take a gamma way

remember that high frequency and now we know high energy

light

well

here is a radioactive source

this is radioactive c zero one thirty seven in admits

gamma waves

when it

the case

some particularly

dangers to be around this kind of radiation

i'm gonna turn on a detector for the radiation something you've probably heard of geiger

counters you see to use

all the time on the television when you're talking about radiation like turn this on

when it detects photons

of gamma radiation italy

and you can hear

bleeping right now

the reason is there's cosmic radiation around this gamma waves are hitting us all the

time

and the little packets

are detectable by this device

now

there's a lot of them always this is that right

gamma source

so this is intense

radiation compared to the background radiation

and lead to bring that

in front of the detector

and now watch i'm gonna bring the

source closer and closer

and listen

you can see how bright this is

there you know ten or fifteen photons every few seconds and now

really getting almost continuous bombardment at all times already so fast brighter and brighter fish

more intense as you bring the source closer

to the counter

each one of those little blips and individual photon individual particle and individual packet of

light

so we've learned that

light has a particle nature

there's a way of property associated with light and electromagnetic radiation and also a particle

nature packets of energy being carried along the way

a brilliant experiment the demonstrates that property is the photo electric affect

and here's how work to take a piece of metal

now model is an array of metal atoms

and each of those atoms phones on rather loosely to its outer a lecture

that's why the metal conducts electricity those electrons are rather free to move about the

surface

now if you shine the light on that surface

what happens

well you can shine a light of star in wavelength you will bring in a

rather long wave like a red

photon

and when a rat beam of light

hits that

you'll find for many medals

nothing happened

and even if you make the like very bright

very intense

nothing happens

if you bring in a greedy

beam of light

this now has higher energy photons shorter wavelength higher energy

what you fine is the electrons are indeed injected

it says photons are striking electrons and taking them off the metal

you bring in a more intense a green light

and you get more electrons they don't what way faster you just get more electrons

with a brighter light

all with the same kinetic energy

you bring in

blue light now higher energy photons even a shorter wavelength

and you find that electrons with even higher kinetic energy a rejected

and again the same correlation with brightness if you make the like brighter

you get more electrons per second release

so it's as electrons are caught in a well

and there is an energy barrier that so the electrons

next to the mat

you have to overcome that energy barrier to reject the lecture on and release it

from the middle

well

designate this

threshold energy or this

well that

with the symbols p

red light

the four times of read like don't have enough energy to even get out of

the well

so it doesn't matter if there is more of them if there's more intense light

more photons per second

still not of the electrons

leave the well

electrons of

our photons in the green region

so shorter wave like have enough energy

to overcome this

binding energy of the electron being held of the metal

and

a little bit of kinetic energy

more energy still

in blue photons

in jack's

electrons with even more kinetic energy

so it says

the

photons of light

are coming in and jostling electrons like i'm holding onto this tennis ball photons are

coming in and jostling them

the higher energy the photon

the more jostling occurs

until

you get to a photon they can actually

higher energy now

brink

no photon three

of the metal

can i might as well but

if you go to higher and higher energies

bigger and bigger photons in this case blue light

you inject the electron with more kinetic energy

no brightness doesn't matter we said well brightness adjust more photons per second that just

paper i backup

but not enough energy one photon

per lecture on to reject any single electron

but

binning photons high energy blue lights a

comes in and slams that metal

and really stands the electro offline

sorry so a high energy

is what we have

so we can actually plot

we can plot the kinetic energy of the electron

versus the frequency of the light that we shine on the middle

and we know

up to a certain frequency no electrons rejected

and then you reach that threshold will just get that you'll just overcome the binding

energy holding electron to the metal and you start to a job electrons then higher

frequency like

just gives you more kinetic energy in the electro

the energy the phone time we know is age a new

so we can write the kinetic energy that the electron has

is the energy that the photon comes in that minus this binding energy

so only access energy of the photon goes into kinetic energy

so you can write the both energies in terms of photons and you can realise

there's a minimum photon energy required

do we jack electron from the map

if you look at different metals

different males have different threshold frequencies

prince and you could have a metal that's described by a blue photon is the

minimum

photon that injects an electron

and higher energy photons

you

electrons with more kinetic energy

so this problem the for electric affect

helps us understand the particle nature of like

and it's actually albert einstein

i gini assume that this problem

so i just before the for the electric affect was understood in the particle nature

of light was understood were taken

their medals shining lights and increasing the intensity figuring

actually not cost more electrons

but increasing intensity very bright light

didn't do anything

and when you could reject electron

increasing the intensity

didn't increasing energy of electrons you just got more electrons coming off with the same

energy

well

it takes aging is often to look at a

a very troubling problem and see it in a whole new like

and that's what einstein did he said what that looks like

the lights behaving like particles

it looks like little bit some later coming in so bright light is just lots

of bits

but they all have the same energy

so those lots of bits inject lots of electrons each electron with the same energy

so the for electrical fact and albert einstein have helped us understand

the particle nature of like

we're in the demo that with money we set up a photo electric affect experiment

e as white light

impinge and on the metal

in the energy of the photo electrons admitted

are shown on the meter it right

if you put a red filter

in the path

now only read of photons can strike the metal and you can see they do

not have sufficient energy to eject photo electrons

if we go to higher energy photons say

go to yellow lighted that's shorter wavelength and higher energy photons

they may be able to eject photo electrons

and indeed for electrons are omitted

but with a relatively small energy

if we go to a higher still

photon energy green wave links

that's shorter wavelengths still higher photon energy use

we can see

full electrons emitted at a higher energy

now we can still go to higher energy photons

blue

photons in the blue region

are the highest energy visible photons and honey has a blue filter that will pass

only blue photon

putting a blue filter in the path

shows photo electrons emitted at the highest energy

so here's an example of the photo electrical effect

thank slightly for that great demonstration

let's talk about the full electrical fact in terms of it can quiz

if we shined a beam of light on a certain metal it has no effect

the question i have for you is what change in that be should i make

in my best hope to eject electrons

should i increase the intensity of the light

the increase the

wavelength of the light

increase the energy

of the like

think about that per minute and make a selection

concerning is

possible arguments for each of the answers

survey

increased intensity means morpho time strike electrons increasing electron kinetic energy

decrease in the way like increases the photon energy which increases the kinetic energy imparted

the electro

or c

increase in the energy of the photons increases the kinetic energy imparted to be electrons

consider those arguments

and make your selection again

when you think about the photo-electric affect you think about the

energy the wavelength the frequency all those are related

of the photon striking the metal

if you have a photon that won't inject electron what you need

you need photons with more energy you have to increase the energy the photon

increasing the number of photons won't do

you'll just track a lot of electrons with a little bit of energy that doesn't

help you

so increasing the intensity is not gonna work

you want more energy in each photon

the energy photons is age new or h c overland that so it inversely proportional

to the wavelength

directly proportional to the frequency

so if you want to increase the energy you should decrease the wavelength

increased energy photons will work

answers at but

if you are clever you also noticed

i'd decreased

wavelength in the photon will also work because that will increase the energy

so here you could have answered b or c

and you would have got an electron ejected from that now

let's look at the for electric affect again

which combination of a photon striking a metal

it jack select run with the highest kinetic energy so i have to nettles represented

and several different

photon energies

so is of the yellow photon striking middle one of green photons tracking metal one

or a blue photon

striking that'll number to think about that for a second and make a selection

let's consider an argument for each of the three answers

yellow light

is high energy

with a lower threshold metal

so it'll give the highest kinetic energy electro

or b

green light is higher energy than yellow light and the striking the same l

blue is tracking a higher threshold metal

so green under the one should be dies or

blue light is the highest energy of all three folder

so which reject electrons with the highest kinetic energy

think about those three for a minute and make another selection

so which combination of photon in metal gives you electron with the highest kinetic energy

let's look at all three

yellow light striking metal one well i kind of outline

about where

the frequencies are of course a single frequency can't

encompass the whole band of green in the whole band of blues

the largest yellow is somewhere below the green that's all we know

so it somewhere in here

so the largest possible in yellow photon

striking that'll one

we give a kinetic energy here

what about green striking metal one

but we know the green photon will be higher energy

then the yellow photon

striking metal one will give a higher kinetic energy

what about blues photons tracking metal to well here's the blue region

so somewhere in here will have a photon

but no strike this metal with a high here

threshold energy

so you can drink the kinetic energy right off the plot

so a blue photon even though it's the highest energy is tracking a higher threshold

metal

resulting in low were kinetic energy portal electron

green

light on metal one will give the highest energy

electrons injected from this metal system

light

has both the properties of a wave

and the properties of a particle

it's a way even a particle at the same time there's a duality to the

way particle relationship

what properties like wavelength

and frequency and speed

somehow must be related to particle property

particle properties that are moving

the most important property is the momentum

it's mass times its velocity

so how do we reconcile the two

well

light

photons of light

carry no mass

so how can i carry momentum

well they carry relativistic moment them

their energy is given by h new or h c overland

the energy can also be expressed

by the and c squared

relativistic energy

well we can cast that in terms of the relativistic momentum

so a single quantity and this p

so using those two relationships we can derive that the momentum

he's

planks constant divided by the wavelength

so here's a single relationship

that shows

particle and wave nature

in the same relationship

so particles and waves a duality

the wavelength is related to the momentum the momentum is related to the wavelength

for light

bunks constant

unites the two

six point two six two times ten to the minus thirty four jewel seconds

way

particle

acting together

sometimes the properties of the particle

exert themselves

sometimes the properties of the wave exert themselves

they both exist together all the time particle and wave nature of like

we've talked about four times as the smallest particle of light

and we said when you get down to the photon level if you split that

photon further it loses the properties of that like

and indeed

splitting the balloon photon

in all their photons is possible

but it no longer has the properties of the balloon like that originally had it's

the smallest particle of blue light

but you could have

but splitting it is still possible

so let's talk about that

a photonic four hundred centimetres

is split into two

one of the photons the comes out is that well on an animator

what is the wavelength of the other photon

let's consider that is it at

two hundred animators be six hundred or seen eight hundred animators

what is

that other photon think about that for a minute

and make your selection

let's consider an argument for each of the answers

hey

splitting a photon must reduce the wavelet

and two hundred is the only smaller waves

energy is conserved and it is inversely proportional to wave like

so one over four hundred

equals one over six hundred plus one over twelve

or see the sum of the wavelength

must be cancer and add to the long longest we've like

twelve hundred is four hundred plus eight hundred

consider those three arguments and make a selection again

when we split a photon

in to other photons

the total energy that we start with can be lost

so energy will be cancer

so the two smaller photon energies

must add to the original photon energy

and photon energy at as the inverse

of the wavelength

so in d

h t over four hundred

most equal itsy over twelve hundred plus the other photon emitted and that must be

h t over six hundred

so in d

to lower energy photons add to give the high energy photon and the correct answer

here is b

a six hundred animator photon

is split along with a twelve hundred animator photon when you split that four hundred

and a beautiful

let's look calculation involving the full electric affect

injected for all electrons and protons of a certain energy getting a map

we'll take the question

what we have like the radiation must use to eject electrons

with the velocity

given from chromium that'll with a work function that's given

so this work function for chromium metal four point three seven electron volts

is how strongly chromium hold onto it electron

so we have to say well what is the photo-electric affect

the for electric affect we have to balance the energies

remember the photo lexicon fact has

the

kinetic energy of the electron

the

photon energy minus

the work function

for the men

but not a holds onto the electron

but if we bring in a high enough energy photon

we can eject an electron with a certain kinetic energy

so that so we have the fine

let's look at what wave like will work for this problem

and what will do is will balance the energy is involved

with a common unit

and the units we always use r

kilograms

meters seconds and jules

yes i units

now we do that to keep

all the things we multiply together

consistent unit wise

where dimension really consistent

we always use kilograms for mass

so don't just put your masses into your equations with

grams or pounds or some random asked unit

you come across the mask converted to get would right

we come across the distance a like

convert that two meters

at time seconds

and energy

you

that would keep your energies can your units consistent and allow you to do the

calculations correct

so again the kinetic energy of the electron is

the

energy of the photon minus the work function of the metal

we can calculate the kinetic energy of electron we're gonna have to look up its

mass

and use the velocity that we've been given

well use

kilograms for its mass

meters

for the link per second

for the velocity

meters per second square

mass

velocity squared

that's gonna be an energy a kinetic energy so this will be jules

in fact that's how remember the s i units of jewels

i remember kinetic energy is a jewel

and

kinetic energy is mass times velocity squared

so it's kilogram meters square per second squared

so this is then pretty straightforward will look up the

mass someone electron express it in kilograms

express are velocity was given in kilometres per second but i'm gonna converted to meters

per second

to give a units the same

square that that's relatively straightforward eleven point sixteen

jules time standard the minus ninety

tidy number of jewels course of the water

with that kinetic energy

we can continue to balance our energy we know the kinetic energy

is eleven point sixteen times ten to the mine is nineteen jules

the work function we've been given

that's four point three seven electron volts

electron volts of a unit of energy

it's

we kinetic energy than an electron gains

as you accelerated across a potential of one vote

we don't have to know that but it is nice to know that

i can convert jules to electron volts with a simple conversion factor i can look

up in any technical

one point six one times ten to the mighty minus nineteen jules product rumble

we can do that product so the work function in terms of jules

seven point o four times then the minus nineteen you

well rearrange now and saw for the energy of the photo the energy the photon

is the kinetic energy of the electron plus the word function

that has t will eleven point sixteen times ten the might is nineteen jules

and

we're gonna at non of that work function seven point o four times ten the

might is nineteen tools

we can express the photon energy in terms of its wavelength

as well as its frequency

and that has to go to some of these two or

eighteen point twenty can stand for the minus nineteen jules

of course

we can solve a the wavelength now that's just h c over eighteen

point twenty times ten the midas nineteen jewels and we can do that matter

this number plug in

blogs constant and the speed of light in jules per second and meters per second

and then we'll notice that the units of jules will cancel out

and the units of seconds will cancel out and levers units of meters

and that we want always good to check

due to units that we have laughed

makes sense for the quantity that we're solving for

we're solving for wave link a link

do i have meters

in this case i do

i have

doing them at hunter nine times ten the minus nineteen

meters

should be hundred

nine times ten the might is nine meters at an animator

under nine animators

is as we recall

in the u v the ultraviolet region

we know visible went from seven hundred down to four hundred millimetres

well all four hundred animators at higher energy

are the ultraviolet photons

so an ultraviolet photon

is required to reject

an electron

from chromium at all

so we understand light

as behaving like a way is like an ocean

with a wavelength and sp but also like a particle a little packet of energy

and the energy amount is each times new punks constant times the frequency of the

now

a particle

has momentum

and we've seen the momentum of the particle that photon

can cause an electron to be rejected from the metal

we saw in the photo like to contact

incoming photon injecting electrons from a metal

how does that particle nature and wave nature reconcile themselves

well let's talk about that

the

light

way particle duality

you have

like that is like a wave we understand with a wavelength

and of frequency and this me

we can write down it's

energy as a particle

as h times new

and

each time see over lambda

using the waves properties to write the energy in two different ways

now the

wave particle the light particle that we call a photon

has a momentum we've seen it can transfer momentum

from the photon to the electron

but the momentum

we often associate with mass

but

the photon has no mass

the photon is a particle

and it

mass less moving at the speed of light

but we can say the energy of the particle use

einstein's

equation for relativistic

particles moving here the speed of light

and c squared is at the energy

now we have to expressions for the energy the energy of the photon and the

relativistic energy and c squared

mass

times velocity

mass times the speed of light c in this case for a photon

can be written as

the moment sometimes seen so

the momentum is

and times c

times another cu gives you and see square

so these expressions for the energy

a pull into these expressions to the energy so what we can do is write

the momentum then

in terms of these two energies and we'll find the momentum

the

points constant divided by the wavelet

a simple relationship

but wean

the momentum and the wavelength

the particle characteristic momentum

and the wave characteristic the wavelength

both expressed at the same time waves and particles

acting

the way they choose

sometimes like will be like a way sometimes a behaves like a particle

there's a duality between them

expressed by this beautiful relationship between the wavelength

and the momentum

bunks constant again extremely small number is the proportionality constant between the momentum and

the wavelength

so waves

particles

light

we have to think of them all at the same time

light

behaves like a way

and a particle

and we came up with a beautiful relationship between the particle nature its momentum and

the wave nature of the wavelength

it be interesting to say let's go back to particle

could be possible that particles have wave nature

we were little surprising we saw

the wave like property light

have a particle nature

is the dichotomy gonna continue

is eight particle

able to have a wave like property

well we would define it in the same kind of way we would say a

particle has a momentum

and electrons for instance they can move

and they'll be moving at a certain velocity you take the product in their mass

in the last me that some momentum

way of would have a weighting the like

if we say well we had this relationship that had

wavelength and momentum in it

to relate

for light

the duality between the particle wave nature

the same thing can be applied to matter

and this is actually very fascinating concept how can a particle like an electron

also behave like a way

i think you can kind of by the light argument like behaves like a weight

and we saw with the fraction interference

we had one with going like this and one-way point like this

when they came together and they added constructively you gotta bright spot

when they added these productively you got a dark spot

and that was very wave like

we saw their particle like nature of light in the photo-electric affect

particles

from matter that's obvious if there is a particle of matter

there's particles of matter atoms electrons fundamental particles

but will they also have a wavelength will there be did duality here

it turns out there is it's one the most fascinating properties of nature that very

tiny particles

have

a wavelength associated with them

we associate the wave like to the same relationship we used for light

we call this that the role be relationship the momentum and the wavelength related

for

particles

we're gonna use the intensity of their way

squared

as the probability of the particle being found in that region

we'll talk about

squaring the wave function of a matter

to get the probability whether that matter actually exists there

so waves and particles

two

totally the similar things but

the

particle and wave the welding works for matter

how can we prove

well remember how we prove that like behave like a way

shined the wave through some obstacles we got this the fraction interference pattern

bright spots and light spots on the scree that's it'll but that's a wave like

property

matter we understand as a particle already

can we just demonstrate its wave like nature

what turns out you can and you can take electrons

and you can shine electrons at little obstacles in this case you use the spacing

between the layers in the crystal

you shine an electron at that

and that the

gives you the fraction in interference

and if you shine that on the screen like you did with the

the light

you find that there's places on the screen that the electrons hit and you get

bright spots lots of electron sitting in certain spots and places on the screen with

a light does not

the

the electrons

passed through their grading their crystal there it's very likely to hit itself some spot

it's unlikely to zero probability that they'll hit other spot

and that's very strange

if you take just the b gun

or machine then you should it through an obstacle there's no place a be on

the slits where the

well it's cannot yet

there's no excluded particles there's always put it space where you cannot hit

with electrons at a different story you passed through that rating you passed through that

crystal

and there are places where the electron is forbidden to hit

there's electrons interfering with each other

you're allowed to hear you're not allowed to hit here there's

dark and light spots that

detect the electrons

high intensity of problem high intensity high probability finding electron in certain spots

low probability dark spots in other spots on the screen

electrons be anything is

their interfering with each other

just like they have a wave property

fantastic property of electrons that we can actually demonstrate

so it's easy to show

electron

give you a probability distribution

you'll have

electrons

going through their crystal braiding

likely is very strongly to hit it some spots on likely to hit other spot

matter

electrons in particular this playing

wave like proper

particles

can behave like waves

they can have a way like property

and the way like property wavelength is given by the broadly rate relationship a particle

the has a momentum

amassed and a velocity will have a wavelength given by the momentum

planks constant divided by that we've like

let's look at some concrete examples

to see actual particles and what they're the probably with like would be

here's a list of particles and their to probably wavelength of proton

now that's a particle of light

that obviously has a wave like that we've talked about a yellow photon it's the

probably wavelength six hundred nanometres

how about an electron moving at end of the fit meters per second

electron just zipping along in space

you can use of the probably relationship

the find a

the probably wavelength

of around six centimetres for that electron

a sony an atom

eight hundred

or at calvin

that's a temperature

that if the time determines the average speed in the system

the average speed of those particles around three hundred meters per second

we know they're sodium adam so we know their mass

but momentum i can calculate a wavelength

a few hundreds of an annotator

now let's take a baseball and of an object that we know the size and

mass out on a macroscopic

object

a macroscopic object like a baseball a hundred and seventy grams set

by the

major league baseball association

a standard baseball rolled at forty meters per second

that's a very good fast ball

we can calculate using an appropriate relationship the wavelength

but look at how small the number

this is tend to the minus twenty six an animator we're already at an animator

stand of the mind is not

now we've gone

that tend to the minus twenty six of the rules

this is incredibly small distance

it is so small it is insignificant

and that's what you say if you take a macroscopic objects by take is

tennis ball and i throw it i get a velocity

i don't notice a wavelength

and you don't notice the with like because the way like there's vanish really small

in order for the wave like properties of matter to manifest itself the matter must

be very tiny

if you have very tiny matter with very tiny moment

then

the wavelength

creeps up into a region where you could actually detected

particle and wave nature of matter is gonna be important for small particles but not

for macroscopic large particles we don't even notice

particles

all electrons

small atoms have we like properties let's look at that in terms of it can

quit

how many photons

they're gonna behave like particles should about its a

that's only an atom

at calvin

the

sodium adam

impacted by

the wavelength of light behaving like a particle behaving like a photon

about how many will start that

about one about a hundred about ten thousand

think about that and make your selection

let's look at possible explanations for each answer

a one particle

well interactive one-way by that are probably relationship so to be a one-to-one relationship

a hundred photons reduce the temperature about a hundred k

that's near zero and the sodium adam should be about start

or c

this only madam wavelength

is about one ten thousand the photon wavelength so sent ten thousand four times are

needed for you will transfer of moment

think about those three explanations and make a selection

matter has both wave and particle characteristics

we seen the

momentum and the wavelength

are related by the to probably relationship

and we calculated it for several

different objects

now we're saying

well as only a madam

is gonna be travelling at

about three hundred meters per second it's gonna encounter photons of six hundred

then a meter waveline

about how many photons have to strike those only am atoms to get them to

slow down

in about stuff

well if you look at this

here's the sodium adam

travelling at

at k that's its temperature at about three hundred meters per second in has a

wavelength as we've seen abouts extensive in and are six hundred seven and you're

those

photons

of yellow light coming in at six hundred millimetres we can say well i want

the moment

of these two systems to be equal i wanted transfer enough momentum from these waves

two

stop

the particle

the way as a particle nature

it has a tiny little momentum

i need to transfer it to this larger momentum your consists only mammon i one

that

keeping with four times and tell

that's only in atom about stops

and i can do that i just calculate the moment of each and as i

do so i see if the moment are related by the wavelength by the role

be relationship and we can see

the momentum of

the

photons

are about ten thousand times smaller than

the moment of

this only a matter

so what i near about ten thousand

four times to about star consortium

you can actually do this experiment it's

that i do this

the

this

experimenter to do this

were awarded the nobel prize

for what's called laser schooling

you can take

atoms and slow them down the smallest lowest temperatures ever achieved

by calling things by traditional means

in refrigerators and by vacuum pumping

and then using this additional method using lasers

the trap the atoms and bonds photons off them to leave virtually

come to a stuff lowest temperatures ever achieved by what's called

laser cool

the correct answer for are laser cooing experiment is about ten thousand yellow photons

the stuff that's only that

we're in the demo that with honey i best in to give us a demonstration

of quantisation of waves

see what you can come up with

he's got to tennessee spins it we get a total

i are

here

all

so five distinct tones rather than a continuous

so we see quantisation of the with links that it in the length of that

too

quantisation of acoustic waves

particles especially tiny ones have a way like property that we can result

and we saw that with electrons going through a crystal

the for acting

some particles

of the wave hitting it some portions of the screen

somehow any other portions that screen

some portions of the screen forbidden to hit

it's if the electrons

come through

interfere with each other like waves and are low only allowed to hit certain

points on the screen

i think it's a little spoke you than that

if you send the electrons through this experiment

one electron at a time

base still

can not yet certain parts of the screen

i think you can imagine all electrons a lot of them behaving like waves and

interfering with each other

but the electrons behaving like both particle and wave when they go through that grading

they somehow no

not to hit certain parts of the screen

it's a very

spooky property of matter

and from here on in chemistry we're gonna talk about those various key quantum properties

of matter

let's start by looking at a classics experiment or classic calculation of particle in the

box you can imagine taking a particle that has a wave like property and trapping

in a small region of space

when you trapped in a small region of space

you get we like properties occurring

and those with like properties are well defined when you trap

the particle

now

you trap the particle in space let's drop picture of that

a wave like

particle

trapped in space i'll draw like yes all say

blocks of length l

and the particle has to me between here and here

it'll have a way like property so i'll draw a wave like expression

on this box

now

this way like expression i'll call the weighting function of that particle

the wave function of that particle

will you have the designation side

in this case i of x because this is the x dimension in space

now we've already said that the intensity of the wave squared

is going to give us

indication of the probability of finding the particle

the probability

size where gives us the probability of finding the particle

clearly in this case the probability flying in the particle rate the middle of the

box

would be very high if this particle behaves like a way

well how do i come up with these way functions

well i can actually do some that max i can say

write down the physics

the kinetic in the potential energy of the particle

and the boundaries that and putting on the particle

and when i do those things

i can solve the differential equation

for the particle

stuck in this tiny little box

it's behaving like a wave their those wave functions i

these are how the wave functions i must interact with each other

if it's a particle to be stuck in this box

now

we will go through all the mathematics but you can solve this

and when you solve this equation you get an expression for side it's not that

harder to heart understand and it looks

like a weighting function is a sign function of oscillating

sine wave

that you recognize junior high school mathematics science axe

is sign of x

the length of the box

is in there and another parameter and is in there there's not just one solution

to this expression there's multiple solutions

on the integers and

work

and give you a solution to this equation

so that means there's not one-way function that works there are several wave functions that

work

you can have a ground state the smallest value of and

but you can have what we have excite what we call excited state higher values

of and

also give weight functions and you can tell what happens this value and is here

in the sign expression is that integer and gets larger you get more

waves appearing in your box

so these functions

so i

give us the probability when we square them of finding the particle at various locations

in the bar

we can also say well what's the energy of that article

we can calculate the energy using our expression for the wave function in the probability

square

and we can say well i'll ranking the energy these particles increase in energy as

n increases

the expression for the energy of the particle

in terms of this

quantum number we're gonna call it now and

go like

the energy of the and state and square h where

over eight and elsewhere the length of the box the quantum number punks constant are

all in there

so i can then plot out well the lowest

energy state

and equal one we have no an equal zero state any one is where we

start our county

and equal to higher energy state

you'll see and goes in as the square

higher and higher energy state

any will three

well also caught calculate and catalogue what we call the no

the areas of the box where there's zero probability

of finding a particle

zero probability are the places where the weight function goes to zero

after you square zero you still get zero

so the probability of finding the particle at these

crossings

is zero

and that's a strange characteristic

of particles that behave like way there's

portions of the box

where the particle is forbidden to be

so this is interesting

i'll have to nodes one two

note a area where the wave function goes to zero in the high energy state

one note here and zero nodes here

when the number of nodes increase the energy state increases that's a higher energy situation

so here's what i have i have a way

i'm bounding it

on either side

and like is on the demonstration when you have a way like property

you bounded on either side only certain wavelength can exist

half a wavelength one full wave like

one and a half wavelength

i can't

one of the third wavelengths in this box

or a quarter of a wavelength because though

particle has to go to zero probability at the ends

so five

the ends of the box

i put boundaries on a way

i naturally get

what i call quantisation

not every wave can fit in these boxes only certain in waves can fit in

these boxes and there's a gap

i go from here

any point one

although we have to here and i skip all those energies in between

i can only have this energy states in the box

all this energy state for the box

and no energy states in between energy is one time

and wayne's naturally do this

it's not unusual to see it we can demonstrated with a new ways

audio

sound

is a way of like property and here's a two

a fixed like

so if i one way is to exist on this to only certain wavelengths will

fit

i'll be able to fit

no full wave on this or wave on this away even have on this

so only certain

sounds

will fit

in this too

as interesting characteristic i can demonstrate a couple of the sounds

that fit in this too

we won't here when we when we

figure the sounds that fit in this too

we will hear continuous sounds we all here who h

in tenuous wavelength

well have

and

to individual wave likes that fit in this box

that's actually demonstrate that i'll try to spin this and you guys can listen

there's one way

no way it's and a you're higher frequency lower

way modeling

and there's that low frequency

long way

to energy levels and you can see energy takes be more energy that high frequency

in this

low frequency on a regular higher

i higher one

that lpc wonderful acoustic example

of ways and quantisation

all you need to get quantisation is take away

and

force it

to exist in a certain area of space

you fix the ends of the way you get quantisation

you take nothing else home from cam one

take on the fact

that when you take away and use

stick boundaries on it

you naturally get quantisation where whether it's a matter way than electron stuck in a

box

or the acoustic way

existing in this little primitive instrument

matter as way like properties

and waves are bounded you get quantisation

you get particle in of a

if i have a particle that has way like properties and strapped in a box

we understand that has different energy states

and how do i make a transition between one energy state and the next energy

state

well i have solar energy and absorb amount of energy equal to the gap

between

those energy states

so let me ask you

which is true about the photon energy i could absorb the energy in terms of

photo

absorbing each transition shown so here's transition a and transition be

so a particle of you know

box like l and a particle same article

bigger about

no i haven't drawn in be to scale the question is which transition is bigger

has a larger energy transition is a bigger than be are but are they about

the same

is a smaller than b

think about that for a minute and make a selection

that's looking up

possible explanation for each of the answers

a smaller box size means a larger spacing of the energy level so a is

gonna be bigger than b

for b

twice the box like means double the energy so the transitions should be about equal

or c

and equal to for ling the box

is equal to any people for it to l box

but the ground state slower

to l

we'll have be larger

then a

think about those

and make another selection

we're looking at identical particles trapped into different boxes one box twice the size of

the other box

if you look at the particles trapped in the boxes and you excite them

you say go from

the n equal one ground state to the n equal to excited state for instance

for the small box

what is that look like

well

you could calculate the energy is based on this expression

but you could also just look at the energy levels of both boxes here's any

well one for instance

for the smaller box

and in table two

for the smaller box

any well one

for the larger box here

and n equal to for the larger box and years when you notice something interesting

if n equal to

and you put that into the expression you get a

to hear and the two l here

that actually energy level lines up with the n equal one case for the smaller

box

because you'd have a one here and a one here

so you get

cancellation in the two case

for both

though larger box

and n equal one case for the smaller

those energy levels turn out to be the same

if you look at the

any well for case

that lines up in energy with the n equal to case for the smaller but

so what you have are

a transition between two and four

would give you equal energies but a transition between one and for the large box

is bigger than

one to two

for

the small

so the correct answer here

a transition

smaller than the transition

if you take a particle

the behaves like a wave

and you trap it you put boundaries on it you trap and in a box

it turns out you can only have certain energies

it's not like when you take a more able

and you put it in a box

and you shake the marble around it can have manual kinetic energy it once

really fast giving going slowly can be going to continue is

amounts of the last these in between

that's not true

for a particle the bayes like away

particles would be like a wave can have only start and energies

the energies are quantized

remember way

plus boundaries gives you quantisation

i have some quantized levels written here and quantisation is the fundamental property that allows

absorption and emission alike

because

if you're going to make the system go from

one level to the next

you can't absorb just any old wave like

you have to absorb the wave like that actually gets that gives the exact amount

of energy to go from

low state the high energy state

all other energy levels

and all other energies

that the system experiences will be ignored

but

energies that

it's energy map

energies that mapped onto this

will be absorbed or

conversely emitted

so here's a wavelength

high energy wavelength

exposed to this system but there is no

spacing energy spacing equal to that energy so that is

transmit

here's only a wave like that exactly matches

this high energy transition that will be absorbed

and was absorbed from the spectre you see it's missing

in the continuous band that's being exposed to the matter

that wavelength is absorbed you'll get a dark area where that we've like there's absorb

because

the system

as an energy weight energy spacing that matches that frequency

and of course

atomic and molecular transitions work like this

you'll have

some wavelengths

that will pass right through

some wavelengths will be absorbed

it's like the goldilocks principle of atomic absorption

some wavelengths are to be

some are too little

some

are just right

so you have another just right that will be absorbed

and perhaps of find a third

just right

energy level that will be absorbed so you get an absorption spectrum that says this

would this yellow in this red are removed

from the continuous

like that's eating this object

or you could have the light

emit

by the system the system could in minute

the

energy of

the highway of like and then you have a single emission it can in the

all

we've likes of like only sort

with length of like are in it

and this is why things can have certain colours

because the little in emit certain wavelengths of light

here at this example

a blue wave like

a lower energy green wave like and the still lower energy red wavelength

absorption and emission

of light

by objects that are bounded

bounded say electrons

in a box

have certain energy levels

therefore

certain

absorption

and emission frequency

matter absorbs or emits light based and it's

fine electronic structure that is you have electrons behaving like waves there are bounded in

the matter

so they have only certain energy levels that can exist and all these certain transitions

they're allowed to be absorbed

automated

five four times stimulating that

now let's take this

let's say a certain piece of matter has this

energy level scheme that shown here

and it has and emission spectrum

which of these to me emission lines

arises from the transition of

high energy to low energy three to one

emission in this system

is that a beer c

think about that for a second

and make a selection

let's look at possible explanations for each answer a

it is the highest frequency transition so it also has the highest energy and three

to one is the largest energy spacing

or b

means in the middle and transition three to one has an energy level in the

middle so there's a similarity between the energy levels spacing is and the spectrum itself

or c

c is the highest wavelet

and therefore highest energy transition and three to one is a large standard space

think about those three options

and make a selection

we're trying to get from the energy levels space things

in some matter to the actual emission spectrum

that we observe

if you look it impossible energy transitions

a transition between level three and two is possible that would be the lowest energy

of the possible that the smallest

spacing here so that's the smallest energy

so on a frequency plot it would be a lowest frequency

or highest wavelet

if you look at the transition from two to one also possible

that some think your energy spacing

higher frequency

the other transition from three to one is the highest

possible for this system

three to one would give you a line at a

a here the highest energy transition is the highest frequency is the correct answer

let's look at and

energy level

spectrum

so some energy that's in minute or absorbed from a system and try to predict

what the electronic structure what this these things are

in that actual system of matt

so the reverse of what we did last so

to which energy level scheme a mere see there's this emission spectrum

correspond

think about that for a minute

and make a selection

some possible explanations for each answer a when you flip in energy level diagram ninety

degrees that's a good way to arrive at what the spectrum looks like

too small transitions give the same low energy light and three unique high energy transitions

give the higher ones

or c

there are three large energy spacing and one small and the spectrum has three high

and one low energy like

think about those three possible explanations and make another selection

let's look at the relationship between emission spectra and energy level spacing in the matter

if you have a

energy level spacing that looks like a what with the emission spectrum look like

we have to look at every possible transition in the system

and here you can see three high energy level transitions

those would give you high frequency lines

and three low you could have this tiny transition this tiny transition and this tiny

transition

needs to of equal energy so they're degenerate

they would fall right on top of each other and give you only one why

even though there's two

transitions

but the two transitions have the same energy

so we can't was all of them in terms of energy

so you get just two lines one for

this transition and one corresponding to both of these transition

so that doesn't look like the right answer

if we look at

b we have

one two three

for transitions

but these and then it'll to

are the same energy they would fall right on top of each other

so you have a very high energy level a medium and the medium at the

same energy and the low

in your

high band that's a total of three

from these for transitions

since two are exactly the same

and then to tiny

low energy transitions but again they are of equal energy

so that would give you one line

that looks like the spectrum we've seen

and if you look at see that of course isn't anything like what we see

you have one

large energy transition and then

two

energy transitions in the intermediate range but this one this here and this pair

are equal energies will give you only one line so this very gives you one

like this very give you one line

to intermediate lines and then a small feature

so you see i you can

analyse

energy level diagram and go to a spectrum

in kind of backwards and forwards that's why i s

spectrum

is valuable it tells you by inference

something about the actual matter

and remember you can look at tiny little matter in your microscope you have the

baby that with this electromagnetic radiation

see what it absorbs and the minutes

and bile thinking about what it absorbs and the minutes reconstruct

what its energy level diagram what it

might be

what it's electronic structure might be

so here

the correct answer is b

lun is in the demo that preparing to demonstrate laser induced fluorescence

fluorescence occurs when high energy photons

or absorbed

and a lower energy photons are emitted

lenny will start with an ultraviolet loser that's higher energy then the visible region

as the ultra violet laser passes through this blue solution

ultraviolet photons are absorbed and blue photons are emitted

here ultraviolet photons are absorbed

and photons in the green are emitted

here ultraviolet photons are absorbed while four times in the yellow are emitted

and ultraviolet

photons stimulate the emission of photons in the red region in the final solution

now let's try that same experiment

with a lower energy loser

this is blue in the visible region

in order for fluorescence to occur

we have to absorb a high energy photon

and emit a lower energy

so here blue laser is transmitted through the blue solution

but

blue photons are absorbed here

and photons in the green are needed

here

blue photons stimulate emission of photons in the yellow

in the final solution

photons in the blue region stimulate emission of photons in the red region

one final laser a green laser

even lower in energy of photons lower than ultraviolet and

blue

photons

be green laser insufficient to stimulate emission in the blue

and the green laser

transmitted through the green solution

and

the green laser

stimulating emission of yellow

photons

from this solution

and

the green laser

stimulating emission of photons in the red region

from the final solution

so the laser induced a fluorescence

demonstrated by losers and a coloured solution

What Is Light And How Does It Interact With Matter? - Lectures on photon emission and absorption

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