Quantum Physics

Question 1

What is a blackbody?

Answer 1

An object in thermodynamic equilibrium which absorbs all radiation incident on it.
It purely emits radiation due to the conversion of the body’s internal energy into electromagnetic energy.

Question 2

Why are stars approximated as blackbodies?

Answer 2

Because their interiors are in equilibrium, with radiation escaping through outer layers.

Question 3

What is a blackbody in the lab?

Answer 3

A closed box called a cavity made of absorbing material at a fixed temperature, with a small hole allowing radiation to escape.

Question 4

What is the boundary condition of a cavity?

Answer 4

That the waves have 0 amplitude at the walls to remain in equilibrium and not dissipate energy.

Question 5

What is the Maxwell-Boltzmann equipartition theorem?

Answer 5

States that energy is shared equally among each independent mode.

For a blackbody, each mode of radiation is in thermal equilibrium with the oscillating atoms in the walls.

Question 6

How does the equipartition theorem lead to the Rayleigh-Jeans law

Answer 6

The equipartition theorem states that the average kinetic energy = (1/2)kT, and average pot. energy is (1/2)kT, therefore Etot is kT.

The energy density is given as du(λ)/dλ, = (Eavg / L^3)|dN/dλ| = (8π kT / λ^4)

using λ = c/ν, du(v)/dv is given as: du(v)/dv = (du/dλ)(dλ/dv) = (8π kTv^2 / c^3)

Question 7

What was the ultraviolet catastrophe?

Answer 7

The result of his equation did not match the measured blackbody spectrum at higher frequencies, and the Rayleigh-Jeans law tended towards infinite energy as frequency increased.

The Rayleigh Jeans law only describes the measured blackbody spectrum at low frequencies.

Question 8

What did Planck initially propose?

Answer 8

That energy states of an atom in the wall is proportional to its oscillation frequency, E = nhv

Where n is a quantum number and not the same as the radiation mode n.

He proposed that the energy states can only take discrete values.

Question 9

How did Hertz show the photoelectric effect?

Answer 9

He used a spark gap generator. A stronger spark was observed when the device was illuminated by visible or UV light.

Question 10

What is observed in the photoelectric effect?

Answer 10

When light is incident on a metal surface, electrons become excited from the atoms and are seen emitted from the surface.

When a positive voltage is applied, electrons are attracted to the opposite plate and produce a current.

Question 11

What is the stopping potential?

Answer 11

When a negative voltage is applied, the opposite plate repels electrons emitted from the surface, so only electrons with a maximum kinetic energy can reach the plate.

Question 12

What were Einstein’s predictions on the photoelectric effect?

Answer 12

A minimum light frequency was required to eject electrons.

Increasing the light’s frequency should increase the electron’s maximum kinetic energy.

Question 13

How does the photoelectric effect provide evidence for wave-particle duality?

Answer 13

If light was a continuous wave of energy, there would be no threshold frequency as over time enough energy would be supplied to liberate electrons no matter the frequency.

Question 14

What was the Compton Scattering experiment?

Answer 14

The wavelength of high energy X-rays was measured after scattering off electrons, and it was found that by applying E = hν, that E = pc. This can be used to derive p = h/λ.

Momentum is conserved through the change in wavelength of the X-rays, and the energy increase of the electron.

Question 15

What happened when Compton used different angles for the spectrometer?

Answer 15

there is a bigger gap between the interference pattern and more distinct peaks.

Question 16

What is a wave packet made up of?

Answer 16

Distinct sinusoidal waves of different wavelengths, which superpose to create wavepackets in regions of constructive interference.

Question 17

What is group velocity?

Answer 17

The velocity that the envelope travels.

Question 18

What is phase velocity?

Answer 18

The speed a phase of the wave propagates in space.

Question 19

What is dispersion?

Answer 19

When a wave packet spreads out as it propagates due to the constituent waves having different phase velocities.

Question 20

What is Fourier analysis?

Answer 20

The study of how sinusoidal waves are superposed to approximate different functions.

Question 21

How does wavenumber correlate to spread of waves?

Answer 21

The spread in width becomes larger. Waves with nearly identical wavenumber gives nearly a pure sinusoidal wave.

Question 22

Describe the electron diffraction experiment?

Answer 22

Davisson and Germer published results of an experiment where electrons were scattered off a nickel crystal.

The electrons had known non-relativistic kinetic energies, so the predicted de Broglie wavelengths were found using this.

By applying the Bragg condition using the known nickel spacing and the angle of the maxima, this wavelength can be confirmed.

Question 23

What is the double split experiment?

Answer 23

Young measured the interference pattern between light passing through two small holes, approximated as slits.

Each slit diffracts and spreads out the waves, which overlap and create an interference pattern.

Question 24

How does intensity affect electron diffraction/

Answer 24

A lower intensity leads to a more random spread of electrons. A higher intensity leads to a clearer interference pattern. It cannot be predicted where each individual particle will land on the screen.

Question 25

What happens if you try to predict what slit the particle went through?

Answer 25

The limit of the Heisenberg uncertainty principle is reached, as there is an uncertainty of ∆y, transferring a random momentum ∆py ≈ h/∆y. The same pattern is expected due to this.

Question 26

What is an eigenfunction?

Answer 26

A function which when the operation is applied to it, it returns itself multiplied by a scalar.

Question 27

What is the born rule?

Answer 27

The number density of electrons or other matter particles is proportional to the square of the wavefunction, therefore relating directly the square of the wavefunction to the probability of finding a particle in that region.

Question 28

What is normalising a wavefunction?

Answer 28

setting the probability to 1.

Question 29

What is quantum tunneling?

Answer 29

Describes the observed behaviour of nuclei and bonding between atoms.

The schrodinger theory was applied to calculate the prob. of part of a nucleus spontaneously escaping from a nucleus.

This shouldnt be possible since the pot. energy is larger than the total energy.

The no. of decays in a fixed time from quantum tunelling matches with measured value.

Question 30

What was Bohr’s model of the hydrogen atom?

Answer 30

1. The electron maintains a circular orbit at discrete distances from nucleus.
2. The orbits have discrete values of angular momentum
3. The energy for transition between energy levels is via emission or absorption of em radiation of E = hv.

Question 31

What was De Broglie’s interpreation of the Bohr model?

Answer 31

For a circular orbit, the electrons tangiential speed is constant, giving constant momentum, corresponding to a constant de Broglie wavelength.

nλ = 2πr = L (standing wave condition)

Question 32

What was the Stern-Gerlach experiment?

Answer 32

A collimated beam of atoms passes through a non uniform magnetic field. The magnetic force will cause atoms to be deflected up or down.

when L = 1, mL = -1,0 or 1.
if L = 0 is used, there should be no deflection due to the magnetic moment. The deflection is caused by the spin magnetic quantum number, so only upward and downward deflection was observed.