Module 7: The Nature of Light Quiz

Test Your Understanding

Instructions

This quiz covers Module 7: The Nature of Light. Answer all questions, then check your answers at the bottom.

Topics covered:

  • Electromagnetic spectrum
  • Wave model of light
  • Photoelectric effect
  • Special relativity

Section A: Multiple Choice (1 mark each)

Question 1

In the photoelectric effect, increasing the intensity of light above the threshold frequency:

A. Increases the maximum kinetic energy of electrons B. Increases the number of electrons emitted C. Decreases the threshold frequency D. Has no effect on emission

Question 2

The Lorentz factor \(\gamma\) equals 2 when velocity is approximately:

A. 0.5c B. 0.71c C. 0.87c D. 0.99c

Question 3

In a double-slit interference pattern, bright fringes occur when the path difference is:

A. \((n + \frac{1}{2})\lambda\) B. \(n\lambda\) C. \(\frac{\lambda}{4}\) D. Zero only

Question 4

Time dilation means that a moving clock:

A. Runs faster than a stationary clock B. Runs slower than a stationary clock C. Runs at the same rate as a stationary clock D. Stops completely

Question 5

Wien’s displacement law relates a black body’s peak wavelength to its:

A. Size B. Temperature C. Composition D. Distance

Section B: Short Answer (3-4 marks each)

Question 6

Light of wavelength 400 nm shines on a metal with work function 2.0 eV.

  1. Calculate the photon energy in eV. (2 marks)

  2. Calculate the maximum kinetic energy of emitted electrons. (2 marks)

Data: \(h = 6.63 \times 10^{-34}\) J·s, \(c = 3 \times 10^8\) m/s, 1 eV = \(1.6 \times 10^{-19}\) J

Use: \(E = \frac{hc}{\lambda}\), \(K_{max} = hf - \phi\)

Question 7

A spacecraft travels at 0.8c relative to Earth.

  1. Calculate the Lorentz factor. (2 marks)

  2. If a journey takes 10 years in the spacecraft frame, how long does it take in the Earth frame? (2 marks)

Use: \(\gamma = \frac{1}{\sqrt{1-v^2/c^2}}\), \(t = \gamma t_0\)

Question 8

Light passes through a diffraction grating with 500 lines per mm. Calculate the angle to the first-order maximum for light of wavelength 600 nm.

Use: \(d\sin\theta = m\lambda\), where \(d = \frac{1}{500 \times 10^3}\) m

Section C: Extended Response (5-6 marks each)

Question 9

The stopping voltage for photoelectrons from a metal surface is 1.2 V when illuminated with light of frequency \(8.0 \times 10^{14}\) Hz.

  1. Calculate the maximum kinetic energy of the electrons. (2 marks)

  2. Calculate the work function of the metal. (2 marks)

  3. Calculate the threshold frequency. (2 marks)

Question 10

Explain why the observation of muons at Earth’s surface provides evidence for special relativity. Include:

  • The muon’s rest-frame half-life
  • Expected classical behaviour
  • How time dilation explains the observation
  • Alternative explanation using length contraction (6 marks)

Answers

  1. B - More photons → more electrons; energy per electron unchanged

  2. C - \(\gamma = 2\) when \(v = 0.866c \approx 0.87c\)

  3. B - Constructive interference when path difference = \(n\lambda\)

  4. B - Moving clocks run slower (time dilation)

  5. B - \(\lambda_{max} = \frac{b}{T}\), peak wavelength inversely proportional to temperature

Q6: (a) \(E = \frac{hc}{\lambda} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{400 \times 10^{-9}} = 4.97 \times 10^{-19}\) J = 3.1 eV (b) \(K_{max} = 3.1 - 2.0 = 1.1\) eV

Q7: (a) \(\gamma = \frac{1}{\sqrt{1-0.64}} = \frac{1}{0.6} = 1.67\) (b) \(t = \gamma t_0 = 1.67 \times 10 = 16.7\) years

Q8: \(d = \frac{1}{500 \times 10^3} = 2 \times 10^{-6}\) m \(\sin\theta = \frac{m\lambda}{d} = \frac{1 \times 600 \times 10^{-9}}{2 \times 10^{-6}} = 0.3\) \(\theta = 17.5°\)

Q9: (a) \(K_{max} = eV_s = 1.6 \times 10^{-19} \times 1.2 = 1.92 \times 10^{-19}\) J = 1.2 eV (b) \(\phi = hf - K_{max} = (6.63 \times 10^{-34} \times 8.0 \times 10^{14}) - 1.92 \times 10^{-19}\) \(\phi = 5.30 \times 10^{-19} - 1.92 \times 10^{-19} = 3.38 \times 10^{-19}\) J = 2.1 eV (c) \(f_0 = \frac{\phi}{h} = \frac{3.38 \times 10^{-19}}{6.63 \times 10^{-34}} = 5.1 \times 10^{14}\) Hz

Q10: Key points: - Muons have rest-frame half-life ~2.2 μs - Created ~10 km high in atmosphere, travel at ~0.99c - Classically: should travel only ~660 m before decaying - Observation: significant number reach Earth’s surface - Time dilation explanation: Earth observers see muon clocks run slow, so they “live” longer - At v = 0.99c, \(\gamma ≈ 7\), so effective half-life ~15 μs - Length contraction (muon frame): atmosphere contracted to ~1.4 km, so distance is shorter - Both frames give consistent predictions

Score Guide

Score Performance
90-100% Excellent - Ready for HSC
75-89% Good - Minor revision needed
60-74% Satisfactory - Review weak areas
Below 60% More study required