vce physics units 3&4 unit 4 head start …...diffraction when waves pass through a gap or, an...

VCE PHYSICS UNITS 3&4

UNIT 4 HEAD START

LECTRE

Presented by:Alevine Magila

OVERVIEW:

How can two contradictory models

explain both light and matter?

2

• Mechanical Waves

• Light as a Wave

• Young’s Double-Slit Experiment

• The Photoelectric Effect

• Wave-Particle Duality

• Light and Matter

OVERVIEW:



3


• Light as a Wave





WAVES

• Waves are the transfer of energy from one place

to another without the net transfer of matter

• Mechanical waves such as sound require a

medium such as air to travel through

4

WAVE PULSES VS PERIODIC WAVES

A single disturbance travelling through a medium is called a

wave pulse.

A regularly spaced wave formed from a continuous vibration at

the source is called a periodic wave.

5

TYPES OF WAVES

• There are two types of waves: transverse waves and

longitudinal waves

• In transverse waves, the particles of the medium

oscillate perpendicular to the direction of travel of the

wave

• In longitudinal waves, the particles of the medium

oscillate parallel to the direction of travel of the wave

6

Sound waves are longitudinal waves!

Water waves/ Vibrations on a string are examples of

transverse waves

MEASUREMENTS FOR WAVES

Period (T): The time taken for a complete cycle measured

in seconds (s)

Frequency (f): The number of cycles in one second

measured in Hertz (Hz)

These two quantities are related by: 𝑓 =1

𝑇

7

MEAUSREMENTS FOR WAVES

Wavelength (λ): The length of a single cycle measured in

metres, m, or the distance a wave travels during one period (T)

Velocity (v): The speed at which a wave travels measured in

metres per second, m s-1. For mechanical waves, such as

sound, this can change depending on the medium, such as air

or water

Wave Equation: Relates the frequency, wavelength and velocity

𝑣 = 𝑓𝜆 =𝜆

𝑇Amplitude: The maximum displacement of a particle on the

wave from it’s mean position. The larger the amplitude of the

wave, the greater the wave’s energy

8

SUPERPOSITION

9

• What happens when two waves interact?

• The principle of superposition: when two or more waves

interact, they form a resultant wave with a displacement

that is equal to the sum of the displacements of each of

the individual waves.

SUPERPOSITION





10

SUPERPOSITION





11

SUPERPOSITION





12

http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html

http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html

INTERFERENCE

• We say that constructive interference has occurred

when the waves have particle displacements in the

same direction

13

INTERFERENCE

• We say that destructive interference has occurred when

the waves have particle displacements in the opposite

directions

14

STANDING WAVES

15

STANDING WAVES

• Both waves have equal amplitudes

• Both waves have the same period and frequency

• What is the resultant wave going to look like?

16

STANDING WAVES

17

t = 0

STANDING WAVES

18

t = 0.25T

STANDING WAVES

19

t = 0.50T

STANDING WAVES

20

t = 0.75T

STANDING WAVES

21

t = T

STANDING WAVES

22

t = 0

STANDING WAVES

23

The blue bold line is a

standing wave.

• Points that always have an

amplitude of 0 are called nodes

(the red point)

• Points that always have the

maximum amplitude are called

antinodes (the black point)

STANDING WAVES

REMEMBER, standing waves can only be formed

by two waves that:

• Are travelling in opposite directions

• Have the same amplitudes

• Have the same frequency and period

24

STANDING WAVES - MODES

• A standing wave’s mode of

vibration describes its

shape

• Mode of the standing wave

= the number of antinodes

it has

25

RESONANCE

Consider a swing that is pushed once and left to swing

The swing will oscillate at its ‘default’ or natural frequency.

By pushing on the swing, we can apply a forced frequency to the

swing.

When the applied forced frequency is equal to the swing’s

natural frequency, we say that resonance occurs.

26

RESONANCE

• Many objects can be made to vibrate at it’s natural or

resonant frequency

• Resonance occurs when the forced frequency on an

object is equal to the natural frequency of that object.

27

RESONANCE

Two important things happen when resonance

occurs:

1. The amplitude of vibration significantly increases

2. The maximum possible energy from the source is

transferred to the resonating object.

28

THE DOPPLER EFFECT

• The Doppler Effect is the apparent change in frequency

of a wave due to relative motion between the source

and the observer

29

𝑣

THE DOPPLER EFFECT



and the observer

30

Ambulance stationary Ambulance moving

THE DOPPLER EFFECT



and the observer

• The Doppler effect only influences the apparent

frequency of a sound – not it’s true frequency.

31

DIFFRACTION

When waves pass through a gap or, an aperture, if the width (sometimes also

called the diameter) of the aperture is a suitable length, the waves experience

a circular bending when they emerge from the gap.

This process is known as diffraction.

Note that in the image below, the lines represent wave crests. The troughs of

the waves are in the spaces in between the lines.

32

DIFFRACTION

• Diffraction is an important wave phenomenon that has important

implications for light and matter later on.

• The extent of diffraction is proportional to the ratio between the

wavelength of the wave and the diameter of the aperture.

33

𝐸𝑥𝑡𝑒𝑛𝑡 𝑜𝑓 𝑑𝑖𝑓𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 ∝𝜆

𝑤

Large gap, only a little bit of diffraction Tiny gap, a lot of diffraction

OVERVIEW:



34


• Light as a Wave





LIGHT AS AN ELECTROMAGNETIC

WAVE

• James Clerk Maxwell found that

oscillating electric and magnetic fields

travel at a speed of 3.0 x 108 m s-1 –

exactly the speed of light!!!

• Light IS an electromagnetic wave

35

THE WAVELENGTH AND

FREQUENCY OF LIGHT

Traditionally, we know the wave equation as

𝑣 = 𝑓𝜆

However, thanks to Maxwell, we now know the speed of

light to be c:

𝑐 = 𝑓𝜆An important feature of this relationship is that c is a

constant and will not change.

Therefore, if the frequency changes, the wavelength will

change. Conversely, if the wavelength changes, the

frequency will change: one influences the other.

36

THE ELECTROMAGNETIC SPECTRUM

37

REFRACTION

• Light travels fastest in a vacuum at 3.0 x 108 m s-1

• Light travels ‘slower’ in more optically dense materials

• Light bends when it ‘changes’ speed; this is known as

refraction

38

REFRACTION

• The incoming ray is referred to as the ‘incident ray’

• The final ray is referred to as the ‘refracted ray’

• Often in optics, we establish an imaginary line called the

normal

39

REFRACTION

• When objects move to a more optically dense material,

they are refracted towards the normal.

40

REFRACTION

• The refractive index, n, for a given material is defined as

𝑛 =𝑐

𝑣

• Where c is the speed of light in a vacuum and v is the

speed of light through the material

41

SNELL’S LAW

• The incident ray and the refracted ray of a beam of light

are related by Snell’s Law:

𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2

42

CRITICAL ANGLE AND TOTAL

INTERNAL REFLECTION

𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2𝑛1 sin 𝜃1 = 𝑛2 sin 90°

43

𝐬𝐢𝐧𝜽𝒄 =𝒏𝟐𝒏𝟏

Total

• Note that there is no total

internal reflection if n2 > n1

DISPERSION

• White light is composed of all the different colours of the

visible spectrum

• Dispersion is the splitting of white light into its

component colours

44

DISPERSION

• Each of the colours in white light has a slightly different

wavelength

• Since each colour has a different wavelength, each

colour will travel at a slightly different speed through the

prism

• Therefore, each colour will be refracted to a slightly

different extent through the prism

45

DISPERSION

• This causes the white light to ‘split’ into it’s component

colours.

• This phenomenon is known as dispersion

46

POLARISATION

• Transverse waves can have many different orientations

• Polarisation is the restriction of a transverse wave to

only one orientation (i.e the wave is only allowed to

vibrate in one direction)

47

POLARISATION

• Only transverse waves can be polarised – longitudinal

waves cannot be polarised

• Light can be polarised, which suggests that light is a

transverse wave

48

POLARISATION

• Sunglasses are one application of polarisation

• Light reflected from an object is typically oriented in one

direction

• A polarising lens can be used to reduce glare

49

OVERVIEW:



50


• Light as a Wave





YOUNG’S DOUBLE-SLIT

EXPERIMENT SET UP

51

PREDICTION

Particle model prediction

According to the particle model, there would only be two

bright bands corresponding to the two slits

52

RESULTS

Thomas Young explained the pattern on the

screen by suggesting that light was

inherently a wave in nature.

53

RESULTS

He suggested that light diffracted through the

two slits, and underwent constructive and

destructive interference, forming the bright and

dark bands on the screen.

54

RESULTS

55

• He suggested that light

diffracted through the two

slits, and underwent

constructive and destructive

interference, forming the

bright and dark bands on the

screen.

• We call the pattern on the

screen an diffraction pattern

RESULTS

Since diffraction and interference are wave

phenomena, Young’s double-slit experiment

provides evidence for the wave-like nature of

light.

56

RESULTS OF YOUNG’S DSE

The results of Young’s Double Slit Experiment were:

• On the screen there are bands of light (anti-nodal) and

dark (nodal) lines

• The fringes (bands) produced are evenly spaced

• The intensity of light is greatest at the centre and

decreases as the bands get further from the centre.

57

INTERFERENCE PATTERNS

When changes are made

to the experiment, the

resulting fringes are

changed. A useful formula

is:

58

𝑥 =𝜆𝐿

𝑑

Where

• x is the distance between two light bands (or the distance

between two dark bands)

• λ is the wavelength of light used

• L is the distance between the slits and the screen, and

• d is the distance between the slits

INTERFERENC PATTERS – PATH

DIFFERENCE

DefinitionAt any point on the screen (P), a wave from slit one (S1) will have

travelled a distance S1P and a wave from slit two (S2) will have travelled

a distance S2P. The difference in the distance travelled is the path

difference,

pd = |S1P − S2P|

We can measure path difference in metres, but is usually measured in

wavelengths to determine if the spot P is bright or dark.

59


60

S1

S2

P

The path difference is given

by

p.d = |S1P − S2P|

CONSTRUCTIVE INTERFERENCE

Constructive interference occurs when the path difference

is a multiple of λ, that is

pd = nλ where n = 1, 2, 3, . . .

This is because at point P, even though the waves have

travelled a different lengths, the waves arrive in the same

phase,

i.e. a trough meets a trough and a crest meets a crest.

61


62

S1

S2

P


by

p.d = |S1P − S2P|

Constructive interference:

pd = nλ

DESTRUCTIVE INTERFERENCE

Destructive interference occurs when the path difference is

an odd multiple of 0.5λ, that is

This is because at point P, the waves have travelled through

different paths with different lengths and arrive in the

opposite phase, i.e a trough meets a crest and a crest meets

a trough.

63

p.d = (n -1

2) λ Where n = 1, 2, 3….


64

S1

S2

P


by

p.d = |S1P − S2P|

Constructive interference:

pd = nλ

Destructive interference:

pd = (n -1

2)λ

OVERVIEW:



65


• Light as a Wave





THE PHOTOELECTRIC EFFECT

• Hertz was experimenting with

a spark-gap generator

• He noticed that when the

spark-gap device was

illuminated with light / UV

light, electrons were released

66

Heinrich Hertz 1857 - 1894


• The photoelectric effect is the

phenomenon whereby high-energy

light is able to eject electrons from

a metal / a metal plate

67


The photoelectric effect experiment consists of 4 main

components:

▪ A metal plate placed at the cathode

▪ A monochromatic (single wavelength) light source that shone

onto the cathode,

▪ An ammeter to detect photocurrent, and

▪ A variable voltage that could provide current in the same or

opposite direction to the photocurrent (if the circuit was closed).

➢Forward potential: the variable voltage would make the anode

positive to help the photoelectrons move from the cathode to the

anode, or

➢Reverse potential: the variable voltage would make the anode

negative to prevent photoelectrons from the cathode reaching the

anode.

68

THE STOPPING VOLTAGE AND

PHOTOELECTRON ENERGY

How do we measure the energy of a

released photoelectron?

We can apply a reverse potential.

The stopping voltage, V0, is the

voltage where no photoelectric

current is detected.

69

THE STOPPING VOLTAGE AND

PHOTOELECTRON ENERGY

• Recall from Unit 3 that W = qV

• For an ejected photoelectron, W = eV0

• The stopping voltage can stop even the fastest moving electron. Hence,

the kinetic energy of the fastest moving electron, EK (max), is given by

70

𝐸𝑘 (max) =1

2𝑚𝑣2 = 𝑒𝑉0

THE ELECTRONVOLT

An alternative way to express energy, is with the non-SI unit,

the electronvolt, eV.

The electronvolt is often much more convenient to use than the

Joule since it can be used to directly express the energy in

terms of the stopping voltage

For example: If for a particular photoelectric effect experiment,

the stopping voltage is 5 V, then the maximum kinetic energy

will be 5 eV.

71


OBSERVATIONS

There are 3, very significant

observations that we can make from

the photoelectric effect:

1. There is a frequency called the

threshold frequency, f0, that below

which, there will be no

photoelectrons emitted.

2. Increasing the intensity of light

increases the number of

photoelectrons released.

3. Photoelectrons are released

instantaneously

72


OBSERVATIONS VS PREDICTIONS

1. There is a frequency called

the threshold frequency, f0,

that below which, there will

be no photoelectrons

emitted.

2. Increasing the intensity of

light increases the number of

photoelectrons released.


instantaneously

73

1. All frequencies of light should

eventually be able to emit

photoelectrons

2. Increasing the intensity of

light increases the kinetic

energy of released

photoelectrons


with some time delay

Observations Predictions

THE PHOTON MODEL

To explain the photoelectric effect, Einstein modelled light as

discrete, quantised ‘packets’ of energy called photons.

The photon model was initial developed by Max Planck, who said

that light photons have energy given by the equations:

𝐸 = ℎ𝑓 =ℎ𝑐

𝜆

…Where h is Planck’s constant, which is equal to 6.63 x 10-34 J s.

Einstein posited that there is some minimum amount of energy

which we now call the work function, 𝜙, that is required to release

an electron from a metal.

74

THE PHOTON MODEL

Einstein suggested that when a light photon

collides with an electron it transfers all of it’s

energy to the electron.

Hence, for the least bound electron,

ℎ𝑓 = 𝜙 + 𝐸𝑘 (max)

This relationship is normally written as

75

𝐸𝑘 (max) = ℎ𝑓 − 𝜙

GRAPH OF MAX KE VS FREQUENCY

• KEmax is the vertical axes and f is

the horizontal axis

• -W (work function, 𝜙) is the ‘y-

intercept’ and f0 (threshold

frequency) is the ‘x-intercept’.

• h is the gradient of the line and

remains constant even for

different W and f0 values of

metals.

76

𝐸𝑘 (max) = ℎ𝑓 − 𝜙

𝑦 = 𝑚𝑥 + 𝑐

OVERVIEW:



77


• Light as a Wave





SO WHAT IS LIGHT…?

Both! Light follows the principle of wave-particle duality - meaning it can behave as both a

particle AND as a wave.

78

THE WAVE-PARTICLE DUALITY

In 1909, G.I Taylor did an interesting experiment with interference

He repeated Young’s double-slit experiment with very dim source of light

This provided evidence for the dual nature of light

79

EVIDENCE FOR WAVE-PARTICLE

DUALITY

• An interference pattern still forms

on the screen – even if only one

photon is passed through the slits

at a time

• The shape of the pattern on the

screen is described by a

probability function

80

PARTICLE PROPERTIES OF A

PHOTON

• Many physicists believed that

since light has energy, that it

might also have a momentum

• Arthur Compton provided

evidence for this in 1923

• Monochromatic beam of X-rays

at a block of graphite

• Scattered X-ray photons of

greater wavelength than the

incident ray

81

PHOTON MOMENTUM

• Equation for the momentum of a photon

82

𝒑 =𝒉

𝝀

PHOTON MOMENTUM EXAMPLE

ExampleWhat is the momentum of X-ray photons with energy 3.68 keV?

83

SYMNETRY OF NATURE

• Famous physicist, Louis de Broglie

• Believed in the symmetry of

nature

• Came up with the idea of matter

waves; won the Nobel prize

84

PHOTON MOMENTUM

• Equation for the momentum of a photon

• De Broglie believed this was a general statement about

nature

• Derived equation for the wavelength of a “matter wave”

or a “de Broglie wave”

85

𝒑 =𝒉

𝝀

𝝀 =𝒉

𝒑=

𝒉

𝒎𝒗

DE BROGLIE WAVES FOR MATTER

For most everyday objects the De Broglie wavelength is much

too small to be noticeable.

Try the following examples:

Calculate the de Broglie wavelength of a 600 g basketball that

is thrown at 5 m s-1

Calculate the de Broglie wavelength of an electron travelling at

600 m s-1

86

DE BROGLIE WAVELENGTH

• De Broglie was making a radical claim: that matter has

wave properties!

• Davisson and Germer validated de Broglie’s ideas with

experimental evidence

• They repeated an experiment similar to Young’s double-

slit experiment, except they used ELECTRONS instead

of photons.

• They found a diffraction pattern, suggesting that the

electrons had interfered

87

DIFFRACTION PATTERNS OF DE

BROGLIE WAVES

Recall that

𝑒𝑥𝑡𝑒𝑛𝑡 𝑜𝑓 𝑑𝑖𝑓𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 ∝𝜆

𝑤

88

INTERFERENCE PATTERNS OF DE

BROGLIE WAVES

• The two patterns will only be the same if the de Broglie

wavelength of the electron is the same as the wavelength of

the X-ray photon

• This is because the diffraction is related to 𝜆

𝑤 .Since w does not

change, the wavelength for both electrons and X-rays are the

same.

• Since 𝑝 =ℎ

𝜆 ,if the electron and the X-ray photon have the same

wavelength, they must also have the same momentum, p.

• However, just because the electrons and photons have the

same momentum does not mean they have the same energy.

89

DIFFRACTION PATTERNS EXAMPLE

ExampleFor the diffraction patterns shown below, suppose the electron has a mass of

9.1 × 10−31 kg and the X-rays have a frequency of 3.0 × 1018 Hz. Find the

energy in eV of the beam of electrons.

90

OVERVIEW:



91


• Light as a Wave





LINE EMISSION

92

LINE ABSORPTION

93

BOHR’S MODEL OF THE ATOM

• An electron moves in a circular orbit around the nucleus (the

electrostatic attraction of the nuclear (+) and the electron (-)

is the source of the centripetal force)

• There are only a certain number of allowable orbits at

different distance from the nucleus which are called n =

1,2,3…

94

BOHR’S MODEL OF THE ATOM

• Electrons do not emit energy (photons) when they are in one of these

allowable orbits and ordinarily occupy the lowest orbit available

(ground state)

• A photon absorbed has exactly the same energy as the increase

(change) in energy of an electron in its current orbit jumping to a

higher orbit

• A photon emitted has exactly the same energy as the decrease

(change) in energy of an electron in a higher orbit falling to a lower

orbit.

95

ENERGY LEVEL DIAGRAMS

96


97


98


99

THE ISSUES WITH BOHR’S MODEL

OF THE ATOM

• Bohr’s model of the atom was a conceptual

breakthrough but it was limited.

• Bohr’s model was only adequate for predicting single-

electron atoms (a.k.a hydrogen or ionised helium)

100

DE BROGLIE’S MODEL

• To resolve the issues with Bohr’s model of the atom, de Broglie

proposed that the electrons orbiting the nucleus were matter

waves.

• De Broglie suggested that the matter wave could only be stable

if it formed a standing wave around the nucleus of the atom.

101

DE BROGLIE’S MODEL

• De Broglie suggested that the matter wave could only be stable

if it formed a standing wave around the nucleus of the atom.

• The only wavelengths that the electrons could ‘have’ were the

ones that fitted perfectly into the orbit.

102

DE BROGLIE’S MODEL IN 2D

103

HEISENBERG’S UNCERTAINTY

PRINCIPLE

Heisenberg’s uncertainty

principle:

The more exactly we know

the position of a particle,

the less we know about

it’s momentum.

Conversely, the more we

know about it’s

momentum, the less we

know about it’s position

104

HEISENBERG’S UNCERTAINTY

PRINCIPLE

• Impossible to know both the position and the

momentum exactly

• The more accurate a measurement of position, the less

accurate the momentum measurement becomes

105

Δ𝑥Δ𝑝 ≥ℎ

4𝜋

THE ENDIf you have any questions from today, or you

feel like I didn’t cover a topic in enough detail

for you, don’t hesitate to ask me!

Alevine Magila

[email protected]

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vce physics units 3&4 unit 4 head start …...diffraction when waves pass through a gap or, an...

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