Topic 1 - Wave Particle Duality

Question 1

What are the 4 main properties of Blackbodies?

Answer 1

1. Surface absorbs all radiation upon them
2. Will tend towards thermal equilibrium with its surroundings
3. Absorbs energy at the same rate it emits energy
4. Emitted spectrum dependent only upon temperature

Question 2

Outline the differences between the peaks of two spectral radiance curves at different temperatures (say T1 > T2).

Answer 2

1. The T1 spectral radiance is greater (higher on y-axis than T2)
2. The T1 peak wavelength, the wavelength at which B is max, is smaller (lies to the left of T2)

Question 3

Wien’s displacement law

Answer 3

λ_{peak} • T = 2.90 x 10^{-3} m/K

Question 4

Stefan-Boltzmann’s Law

Answer 4

Total Flux = [Ω], [0 →∞] ∫∫ B(λ) dλ = εσT^{4}

σ = Stefan-Boltzmann’s constant
ε = emmisivity

Question 5

Express Stefan-Boltzmann’s Law in terms of energy density u.

Answer 5

u = εaT^{4}

where a = 4σ/c

Question 6

Define 1 electron volt and give its value to 4 sig figs.

Answer 6

The work done by accelerating an electron through a potential difference of 1V.

1eV = 1.602 x 10^{-19} joules

Question 7

Briefly define the photoelectric effect

Answer 7

The phenomenon where electrons are emitted from a metal surface due to light falling upon it.

Question 8

Say a metal surface is set up to undergo the photoelectric effect. What happens to the stopping potential V_0 if the intensity of light falling upon the metal surface is doubled?

Answer 8

Nothing - the stopping potential is independent of light intensity. In fact, this implies the maximum kinetic energy of electrons is independent of light intensity too.

Question 9

What is the work function?

Answer 9

The surface potential barrier of a metal, in other words, the minimum energy an electron needs to absorb to be ejected from the metal surface.

Question 10

Mathematically, what’s the minimum energy an electron needs to absorb to be ejected from the metal surface?

Answer 10

eV_0 = hf - φ

1/2 m_e(v_max)^2 = hf - φ

Question 11

Why don’t all electrons emerge from the metal with maximum KE?

Answer 11

1. φ is the minimum energy needed to release and electron - some electrons are more tightly bound to the nucleus
2. Electrons may undergo scattering and lose energy before reaching the surface

Question 12

What is the energy of a photon?

Answer 12

E = hf

Question 13

What is the momentum of a photon?

Answer 13

Well, a photon has a speed v = c and zero rest mass. So

E = m_0 c^2 = cp = hf = hc/λ

Implying that: p = c/λ

Question 14

Define the Compton wavelength and give the value of the Compton wavelength for electrons (3 sig figs).

Answer 14

λ_c = h/(m_0•c)

λ_c = 0.0243 Å for electrons.

Question 15

Describe Compton scattering.

Answer 15

Compton scattering is a particle approach where the photon (E0, p0, λ0) “bounces” off an electron giving it some energy and momentum (E1, p1, λ1). See L2 for diagram.