Lecture 2: Photoelectric Effect & Compton Scattering

Question 1

photoelectric effect first discovered when observed that

Answer 1

ultraviolet light affected the voltage at which sparking occurred between metal electrodes.

Question 2

set up to introduce for explaining photoelectric effect

Answer 2

a vacuum chamber containing a metallic plate (it can be of different materials, e.g. sodium) hit by radiation at a certain wavelength and intensity, and a collector on the opposite side. Both sides are connected to a battery that can apply a voltage difference, and the collector is connected to an ammeter that measures the current of the charged particles hitting the collector.

Question 3

classical expectation of photoelectric effect

Answer 3

The expectation is therefore that the energy of an electron emitted does not depend on the frequency of the light, but on its intensity.

Question 4

simulated experiment: changing the material and the wavelength

Answer 4

nothing happens until wavelength reaches a certain threshold where electrons start being emitted

below threshold freq, do not see emitted e- even if intensity is adjusted

changing the material changes the critical frequency

e- have more kinetic energy when at a lower wavelength (higher freq)

Question 5

simulated experiment: changing the intensity and voltage

Answer 5

+ve voltage: e- moving faster and system reaches a saturation current

-ve voltage: higher proportions of electrons start travelling towards the collector but come back, as now the potential is opposed to the initial motion of the electrons.

egardless of light intensity, we can eventually reduce the photocurrent to 0 with a negative stopping voltage v0

Question 6

the stopping voltage decreases linearly with

Answer 6

the light frequency until it reaches 0

there is no photocurrent below a threshold frequency

Question 7

why we need a quantum explanation

Answer 7

Classical physics does not explain why no photocurrent is recorded above the threshold wavelength: it should depend on the amplitude and therefore on the intensity, according to classical waves physics.

Question 8

Electrons are emitted when a work of at least the

Answer 8

binding energy Eb is paid to free them: this value depends on the material of the metallic plate

Question 9

the minimum work that needs to be done to emit electrons is related to the kinetic energy of the electrons

Answer 9

Eb = hv -W

Question 10

minimum threshold frequency necessary to eject electrons is

Answer 10

vth = w/h

Question 11

extra energy ontop of binding energy

Answer 11

kinetic energy which determines a maximum possible velocity

Question 12

The intensity determines the number of

Answer 12

photons present in the light sent to the metallic plate, so higher intensity means that more electron can be extracted, if the frequency is above the threshold, and the photocurrent increases

Question 13

The voltage can be tuned to increase the photocurrent by

Answer 13

facilitating the motion of electrons incresing the voltage. A negative voltage can otherwise invert the motion of the electrons, and consequently reduce the photocurrent all the way to zero

Question 14

problem with plum pudding

Answer 14

According to classical physics, electrons in orbits (accelerating charges) should emit radiation and therefore lose energy and spiral in to the nucleus. What does prevent this from happening? Classical physics could not provide a valid reason.

Question 15

bohr’s postulates

Answer 15

1. e- move in circular orbits determined by Newton and Coulomb’s laws
2. orbits are quantised, e- can only occupt stable orbtis
   3.e- must emit/absorb energy to move orbits
3. atomic angular momentum is quantised

Question 16

Why did the quantum and classical results agree in atoms with large mass number? And why is angular momentum quantized?

Answer 16

Because in large systems classical physics is a good approximation of quantum physics! This is the correspondence principle

Question 17

Bohr’s correspondence principle

Answer 17

Predictions of quantum theory must correspond to the predictions of classical physics in the region of sizes where classical theory is “known to hold”.

Quantum systems are usually described by quantum numbers
n, and the classical limit should be recovered from the quantum results, for n approaching infinity

Question 18

problems with Bohr’s model

Answer 18

-failed to predict observed intensities of spectral lines
-good for one-electron atoms but limiting for multi-electron
-could not really explain wave-particle duality

Question 19

What happens if electrons interact with light at high frequencies such as X-ray?

Answer 19

reasonable to consider the electrons free, since the binding energy of the atom is very small compared to the X-ray energy, so the interaction between the high-frequency radiation and the electron would result in scattering.

Question 20

Classical expectation: when the EM wave is scattered off atoms, the wavelength of scattered radiation should be

Answer 20

the same as the wavelength of the incident radiation

Question 21

Based on Thomson’s theory (Thomson’s scattering), the oscillating electric field of the incident radiation would make the electrons of the target atoms

Answer 21

vibrate with the same frequency, and these would radiate electromagnetic waves at the same frequency.

Question 22

compton found that

Answer 22

with increasing scattering angle, a second peak was appearing at longer wavelength compared to the one of the incident light

Question 23

This change in wavelength between the peaks of the incoming beam and the scattered one is

Answer 23

the compton shift

Question 24

compton wavelength of the electron

Answer 24

constant in equation
h/mec

Question 25

The wave-like and particle-like properties of light can be related by following equation for the momentum p of the photon,

Answer 25

p=kbar k = hv/c = h/lambda

Question 26

de broglie wavelength

Answer 26

lambda dB = h/p

can also use p=hbar k
where k is the de broglie wavenumber

Question 27

The idea of de Broglie gives a

Answer 27

qualitative explanation to Bohr’s idea of quantized orbits, as the waves associated to the electrons would interfer, leaving areas of destructive interference where “electrons are forbidden”, while only standing waves would be allowed to “fit” in the Bohr’s circular orbits.

Question 28

standing wvaes allowed to fit in bohr circular orbits would be given by a

Answer 28

discrete set of wavelengths that interfer constructively if an integral number of wavelengths fits exactly into the circumference of the orbit

n lambda = 2 pi r (r=radius)

Question 29

The reality is that the Bohr’s model, even with the de Broglie interpretation, still doesn’t capture

Answer 29

he probabilistic nature of quantum physics.

Question 30

why classical physics is deterministic:

Answer 30

given a system, if you have enough information about it and know the physics to describe its dynamics, you can determine what will happen next to said system

the process of observing a classical system does not affect the final configuration

Question 31

why quantum physics is probabilistic (electron)

Answer 31

e- is also wavefunction - a probability distribution indicating the regions where the electron is more likely to b

Question 32

The region of space around the nucleus where there is a high probability of observing the electron (~90-95%) is called

Answer 32

an orbital

Question 33

‘forbidden’ regions around the nucleus are

Answer 33

the nodes

Question 34

Electron orbitals introduced by Schrödinger are characterised by

Answer 34

quantum numbers

Question 35

principle quantum number

Answer 35

n
Indicates the energy level and relative size of the orbital. It can take positive integer values (1, 2, 3, …).

Question 36

Orbital Angular Momentum Quantum Number (l):

Answer 36

Defines the shape of the orbital and can take values from 0 to n-1 for each value of n. Each value of l corresponds to a specific type of orbital (s, p, d, f…).

Question 37

magnetic quantum number

Answer 37

ml
Describes the orientation of the orbital in space and can take integer values from -l to +l, including 0

Question 38

spin quantum number s

Answer 38

for an electron, the spin is 1/2

Question 39

spin magnetic quantum number ms

Answer 39

specifies the electron’s spin direction which can be either + or- 1/2