The questions are on the photoelectric effect test. Take it under real conditions before reading the mark scheme.
Quick answer: Light comes in photons of energy E = hf. In the photoelectric effect a photon ejects an electron only if hf is at least the work function φ, and the electron then has maximum kinetic energy Kmax = hf − φ. This mark scheme gives the model answers and the marks for the 8 questions of the Physics 11-12 test on photoelectric effect, from photon energy to duality evidence, with the equivalent answers to accept.
Award marks for method as well as for the final answer. Accept answers within rounding and follow through an earlier slip. Do not penalise a missing unit more than once in each question.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB E.2
Question 1 Photon energy (2 marks)
E = hf = 6.63 × 10⁻³⁴ × 7.5 × 10¹⁴ = 4.97 × 10⁻¹⁹ J (3.11 eV).
Marking: 1 mark for the formula and substitution, 1 mark for the answer with unit.
Question 2 Work function (2 marks)
The work function is the minimum energy needed to remove an electron from the metal surface. The threshold frequency is the lowest frequency of light that can eject electrons, and φ = hf₀.
Marking: 1 mark for each definition (the relationship may be given in either).
Question 3 Einstein’s equation (3 marks)
E = hc/λ = 4.42 × 10⁻¹⁹ J = 2.763 eV. Kmax = 2.763 − 2.1 = 0.66 eV, so Vs = 0.66 V.
Marking: 1 mark for photon energy, 1 mark for Kmax, 1 mark for stopping potential.
Question 4 Wave model failure (3 marks)
The wave model predicts that energy is spread over the surface and can build up in each electron over time, so any frequency should work if bright enough, after a delay. In the photon model each electron absorbs a single photon; if hf is less than φ, no photon has enough energy, however many arrive.
Marking: 1 mark for the wave prediction, 1 mark for one photon per electron, 1 mark for hf being less than φ.
Question 5 Intensity (2 marks)
The photocurrent is halved, because half as many photons arrive per second. Kmax is unchanged, because each photon still has energy hf.
Marking: 1 mark each.
Question 6 Graph analysis (3 marks)
a) f₀ = 5.0 × 10¹⁴ Hz.
b) φ = hf₀ = 6.63 × 10⁻³⁴ × 5.0 × 10¹⁴ = 3.31 × 10⁻¹⁹ J = 2.07 eV.
Marking: a) 1 mark. b) 1 mark for substitution, 1 mark for the answer.
Question 7 de Broglie (3 marks)
λ = h/(mv) = 6.63 × 10⁻³⁴ / (9.11 × 10⁻³¹ × 4.0 × 10⁶) = 1.8 × 10⁻¹⁰ m (0.18 nm).
Marking: 1 mark for the formula, 1 mark for the momentum, 1 mark for the answer.
Question 8 Duality evidence (2 marks)
The photoelectric effect shows the particle nature of light. Electron diffraction by a crystal or thin film shows the wave nature of electrons.
Marking: 1 mark each.
