Physics Unit 4 - Lorimermetres, m, or the distance a wave travels during one period (T) Velocity...

Physics Unit 4

2017 Head Start Lecture

Presented by:

Alevine Magila

§c 2017 Alevine Magila 3 / 115

Overview: How can two contradictory models

explain both light and matter?

§  Mechanical Waves §  Light as a wave §  Young’s double-‐slit experiment §  The photoelectric effect §  Wave-‐Par?cle Duality §  Light and MaBer

Mechanical Waves Light as a wave Young’s double-slit experiment The photoelectric effect Wave-Particle Duality Light and Matter






Waves

Waves are the transfer of energy from one place to another without the net transfer of matter.

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Mechanical waves such as sound require a medium such as air to travel through.


Wave pulses vs periodic waves



A single disturbance travelling through the medium is called a wave pulse.

A regularly spaced wave formed from a con?nuous vibra?on at the source is called a periodic wave.

Image not available due to copyright restrictions

Image not available due to copyright restrictions

Types of waves

There are two types of waves: transverse waves and longitudinal waves.

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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

§c 2017 Alevine Magila


Types of waves


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Types of waves


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Measurements for Waves

Period (T)is the time taken for a complete cycle measured in seconds (s)

Frequency (f)is the number of cycles in one second measured in Hertz (Hz)

These two quantities are related by:f = 1 T



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Measurements for Waves Wavelength (λ)is 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, ms-1. For mechanical waves, such as sound, this can change depending on the medium, such as air or water

Wave EquationRelates the frequency, wavelength and velocity

AmplitudeThe larger the amplitude of the wave, the greater

the energy



v = fλ = 𝜆/𝑇 

Superposition

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§  What happens when two waves interact?



Superposition

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§  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

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§  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

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Superposition

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hBp://www.acs.psu.edu/drussell/Demos/superposi?on/superposi?on.html



Interference

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§  We say that constructive interference has occurred when the waves have particle displacements in the same direction.



Interference

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§  We say that destructive interference has occurred when the waves have particle displacements in opposite directions



Standing waves



Standing waves



Standing waves

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§  Both waves have equal amplitudes

§  Both waves have the same period and frequency

§  What is the resultant wave going to look like?



Standing waves

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t = 0



Standing waves

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t = 0.25T



Standing waves

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t = 0.50T



Standing waves

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t = 0.75T



Standing waves

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t = T



Standing waves

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t = 0



Standing waves

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The bold blue line is a standing wave.

§  Points that always have an amplitude of 0 are called nodes (the red point)

§  Points where the amplitude of the wave are at a maximum are called antinodes (the black point)



Standing waves

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REMEMBER, standing waves can only be formed by two waves that: §  Are travelling in opposite directions §  Have the same amplitude §  Have the same frequency and period



Standing waves - modes

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§  A standing wave’s mode of vibration describes its shape

§  Mode of the standing wave = the number of antinodes it has



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 equals the swing’s natural frequency, we say that resonance occurs.


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

resonant frequency §  Resonance occurs when the natural frequency of an

object is equal to the forced frequency of an object.



Resonance

Two important things happen when resonance occurs: 1.  The amplitude of vibration significantly

increases. 2.  The max. possible energy from the

source is transferred to the resonating object.



The Doppler Effect

§  The Doppler effect is the apparent change in frequency of a sound due to relative motion between the source and the observer



The Doppler Effect


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Ambulance stationary Ambulance moving



The Doppler Effect


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§  The Doppler effect only influences the apparent frequency of a sound; - not it’s true frequency.



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Diffraction

When light passes through a slit that has a width w that is similar to its wavelength λ, the light spreads out forming a diffraction pattern.

The spacing is proportional to λ , so as the wavelength w increases the diffraction expands and when the slit width increases the diffraction contracts.



Diffraction



Diffraction

Another way to express this is:

diffraction ∝�slit size

wavelength λ = w

w < λ means significant diffraction occurs

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λ < w means less diffraction occurs



Diffraction








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


The wavelength and frequency of light

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Tradi?onally, we know the wave equa?on as

𝑣=𝑓𝜆 However, thanks to Maxwell, we now know the speed of light to be c.

𝑐=𝑓𝜆 An important feature of this rela?onship is that c is a constant and will not change. Therefore, if the frequency chances, the wavelength will change. Conversely, if the wavelength changes the frequency will change: one influences the other.



The electromagnetic spectrum



Refraction

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

§  Light travels ‘slower’ in more op?cally dense materials

§  Light bends when it ‘changes’ speed; this is known as refrac?on



Refraction

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

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

§  OVen in op?cs, we establish an imaginary line called the normal



Refraction

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§  When objects move to a more op?cally dense material, they are refracted towards the normal.



The refractive index

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§  The refrac?ve 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



Snell’s law


§  The incident ray and the refracted ray of a beam of light are related by Snell’s law:

𝑛↓1 sin 𝜃↓1  = 𝑛↓2 sin 𝜃↓2  


The critical angle and total internal reflection


Total

𝑛↓1 sin 𝜃↓1 = 𝑛↓2 sin 𝜃↓2    𝑛↓1 sin 𝜃↓𝑐 = 𝑛↓2 sin 90°   𝐬𝐢𝐧𝜽↓𝒄 = 𝒏↓𝟐 /𝒏↓𝟏   

§  Note that there is no total internal reflec5on if n2 > n1


Dispersion


§  White light is composed of all the different colours of the visible spectrum

§  Dispersion is the spliYng of white light into its component colours.


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.


Dispersion


§  This causes the white light to ‘split’ into it’s component colours.

§  This phenomenon is known as dispersion.


Polarisation


§  Transverse waves can have many different orienta?ons

§  Polarisa?on is the restric?on of a transverse wave to only one orienta?on (i.e the wave is only allowed to vibrate in one direc?on)


Polarisation


§  Only transverse waves can be polarised – longitudinal waves cannot be polarised

§  Light can be polarised, which suggests that light is a transverse wave


Polarisation


§  Sunglasses are one applica?on of polarisa?on §  Light reflected from an object is typically oriented

polarised in one direc?on

§  A polarising lens can be used to reduce glare







Young’s Double-slit experiment



Young’s DSE Setup




Prediction

Particle model prediction According to the particle model, there would only be two bright bands corresponding to the two slits



Results Thomas Young explained the pattern on the screen by suggesting that light was inherently a wave in nature.



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.



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.

•  We call the pattern on the screen a diffraction pattern


Results

Since diffraction and interference are wave phenomena, Young’s double-slit experiment provides evidence for the wave-like nature of light.


Results of Young’s DSE

The results of Young’s Double Split 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.



Interference Patterns

When changes are made to the experiment, the resulting fringes are changed. A useful formula is:

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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.

𝑥= 𝜆𝐿/𝑑 



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Definition At 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.

Interference Patterns – Path Difference





S1

S2

P S1P

The path difference is given by p.d = |S1P − S2P|�


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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.





S1

S2

P S1P

The path difference is given by p.d = |S1P − S2P|


Construc5ve interference: pd = nλ

Destructive Interference

Destructive interference occurs when the path difference is an odd multiple of λ, that is

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where n = 1, 2, 3, . . .

This is because at point P, the waves have travelled a different lengths and arrive in the opposite phase, i.e. a trough meets a crest and a crest meets a trough.

p.d = (n - 1/2 ) λ





S1

S2

P S1P

The path difference is given by p.d = |S1P − S2P|


Construc5ve interference: pd = nλ

Destruc5ve interference:

pd = (n-1/2 )λ






The Photoelectric Effect

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§  Hertz was experimen?ng with a spark-‐gap generator

§  He no?ced that when the

spark-‐gap device was illuminated with light/ UV light, electrons were released.

Heinrich Hertz 1857 -‐ 1894



The Photoelectric Effect


§  The photoelectric effect is the phenomenon whereby high-‐energy light is able to eject electrons from a metal/ a metal plate


The Photoelectric Effect Experiment


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).

Ø  Forward potential: the variable voltage would make

the anode positive to help the photoelectrons move

from the cathode to the anode, or

Ø  Reverse potential: the variable voltage would make

the anode negative to prevent photoelectrons from

the cathode reaching the anode.


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.


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

𝐸↓𝑘 (max) = 1/2 𝑚𝑣↑2 =𝑒𝑉↓0 


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.


The Photoelectric Effect 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.


The Photoelectric Effect 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.

3.  Photoelectrons are released

instantaneously.

Observations Predictions 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

3.  Photoelectrons are

released with some time

delay


The photon model


To explain the photoelectric effect, Einstein modelled light as discrete,

quantised ‘packets’ of energy called photons.

The photon model was initially developed by Max Planck, who said that

light photons have energy given by the equations:

…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.

𝐸=ℎ𝑓= ℎ𝑐/𝜆 


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+ 𝐸↓𝑘 (𝑚𝑎𝑥) 

𝐸↓𝑘 (𝑚𝑎𝑥) =ℎ𝑓− 𝜙

This relationship is normally written as


Graph of Max KE vs frequency


𝐸↓𝑘 (𝑚𝑎𝑥) =ℎ𝑓− 𝜙

𝑦=𝑚𝑥+𝑐 §  KEmax is the ver?cal axes and f

is the horizontal axis

§  -‐W (work func?on, 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.







So what is light...?


Both! Light follows the principle of wave-‐par5cle duality -‐ meaning it can behave as both a

par?cle AND as a wave.


The wave-particle duality


In 1909, G.I Taylor did an interes?ng 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


Evidence for wave-particle duality


§  An interference paBern s?ll forms on the screen – even if only one photon is passed through the slits at a ?me

§  The shape of the paBern on

the screen is described by a probability func?on


Image not available due to copyright

restrictions

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

§  Monochroma?c beam of X-‐rays at a block of graphite

§  ScaBered X-‐ray photons of greater wavelength than the incident ray


Photon momentum


𝒑= 𝒉/𝝀 

§  Equa?on for the momentum of a photon


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Photon momentum Example

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



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Symmetry 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



Photon momentum


𝒑= 𝒉/𝝀 

§  Equa?on for the momentum of a photon

§  De Broglie believed this was a general statement about nature

§  Derived equa?on for the wavelength of a “maBer wave” or a “de Broglie wave”

𝝀 = 𝒉/𝒑 = 𝒉/𝒎𝒗 


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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



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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



Diffraction Patterns of De Brogle Waves

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Recall that

𝑑𝑖𝑓𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 ∝𝜆/𝑤 



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 speed or energy.



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Diffraction Patterns Example Example For 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.








Line Emission



Line Absorption




§  An electron moves in a circular orbit around the nucleus (the electrosta?c aBrac?on 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…

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 emiBed has exactly the same energy as the decrease (change) in energy of an electron in a higher orbit falling to a lower orbit.

Bohr’s model of the atom


Energy Levels Diagrams













§  Bohr’s model of the atom was a conceptual breakthrough, but it was limited.

§  Bohr’s model was only adequate for predic?ng one-‐electron atoms (a.k.a hydrogen or ionised helium)

The issues with Bohr’s model of the atom


De Broglie’s Model


§  To resolve the issues with Bohr’s model of the atom, de Broglie proposed that the electrons orbi?ng the nucleus were ma7er waves.

§  De Broglie suggested that the maBer wave could only be stable if it

formed a standing wave around the nucleus of the atom.


De Broglie’s Model


§  De Broglie suggested that the maBer 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 fiBed perfectly into the orbit.


De Broglie’s Model in 2D



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Heisenberg’s uncertainty principle

Heisenberg’s uncertainty principle:

The more exactly we know the posi?on of a par?cle, the less we know about it’s momentum. Conversely, the more we know about it’s momentum, the less we know about it’s posi?on



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Heisenberg’s uncertainty principle

Δ𝑥Δ𝑝 ≥ ℎ/4𝜋 

§  Impossible to know both the posi?on and the momentum exactly

§  The more accurate a measurement of posi?on, the less accurate the momentum measurement becomes



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Example: Heisenberg’s uncertainty principle

A physicist is performing an experiment with a single slit of width B. A diagram of the set-‐up is shown in Figure 1. The physicist decides to decrease the slit width B. In terms of Heisenberg’s uncertainty principle, explain what will happen to the diffrac?on paBern on the screen when they decrease B.

Figure 1: The experimental set-‐up




The End


If 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]

The End


If 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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Physics Unit 4 - Lorimermetres, m, or the distance a wave travels during one period (T) Velocity...

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