AQA A-Level Physics Paper 1, June 2023: Question 12

1 mark · Medium difficulty · Multiple Choice

Calculate the maximum speed of photoelectrons released from a metal surface given the incident photon energy and the work function.

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Question

Multiple choice question numbered 12. It states: Photoelectrons are released when monochromatic light with a photon energy of 4.2 × 10^-19 J is incident on a metal surface. The work function of the surface is 2.4 eV. What is the maximum speed of the photoelectrons as they leave the surface? Four options are given with checkboxes: A) 1.3 × 10^6 m s^-1, B) 6.3 × 10^5 m s^-1, C) 2.8 × 10^5 m s^-1, D) 2.0 × 10^5 m s^-1.
Question text

12 Photoelectrons are released when monochromatic light with a photon energy

of 4.2 × 10−19 J is incident on a metal surface.

The work function of the surface is 2.4 eV.

What is the maximum speed of the photoelectrons as they leave the surface?

[1 mark]

A 1.3 × 106 m s−1

B 6.3 × 105 m s−1

C 2.8 × 105 m s−1

D 2.0 × 105 m s−1

Mark scheme

Show the mark scheme Mark scheme indicating the correct answer for question 12 is C, with the value 2.8 × 10^5 m s^-1.

12 C 2.8 × 105 m s−1

How to answer it

Calculating Maximum Speed of Photoelectrons

What this question tests

This question assesses your ability to apply Einstein's photoelectric equation, convert units between electronvolts (eV) and joules (J), and rearrange the kinetic energy formula to solve for velocity.

Question 12 [1 mark]

Multiple Choice Question Solution

✅ Correct Answer: C

2.8 × 10⁵ m s⁻¹

Awarded for correctly identifying option C.

💡 Key Knowledge

  • Einstein's photoelectric equation: hf = Φ + KE(max)
  • Kinetic energy formula: KE = 0.5 × m × v²
  • Unit conversion: 1 eV = 1.60 × 10⁻¹⁹ J
  • Mass of an electron ( m_e ) = 9.11 × 10⁻³¹ kg (from your data booklet).

🧠 Exam Technique

For multiple-choice calculations, always jot down your steps and intermediate values on your question paper before looking at the options. This prevents you from falling into common distractor traps set by the examiner.

❌ Common Errors

  • Forgetting to convert eV to Joules: Subtracting 2.4 directly from 4.2 × 10⁻¹⁹ without multiplying by the elementary charge.
  • Square root omission: Forgetting to take the square root of v² at the final stage, which yields a wildly incorrect large number (distractor A).
  • Power of ten slips: Mismanaging indices when converting the work function or dividing by the electron mass.

📐 Step-by-Step Calculation

  1. Convert the work function (Φ) from electronvolts to Joules:
    Φ = 2.4 eV = 2.4 × 1.60 × 10⁻¹⁹ J = 3.84 × 10⁻¹⁹ J
  2. Rearrange Einstein's photoelectric equation for maximum kinetic energy:
    KE(max) = hf − Φ
    KE(max) = (4.2 × 10⁻¹⁹ J) − (3.84 × 10⁻¹⁹ J) = 0.36 × 10⁻¹⁹ J
  3. Substitute into the kinetic energy formula to solve for velocity (v):
    KE = 0.5 × m × v²
    0.36 × 10⁻¹⁹ = 0.5 × (9.11 × 10⁻³¹ kg) × v²
    v² = (0.36 × 10⁻¹⁹) / (0.5 × 9.11 × 10⁻³¹)
    v² = 7.903 × 10¹⁰ m² s⁻²
  4. Take the square root to find maximum speed:
    v = √(7.903 × 10¹⁰) = 281,130 m s⁻¹ = 2.8 × 10⁵ m s⁻¹ (matching option C).

Topics

Physics · 3.2 Particles and radiation

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.