AQA A-Level Physics Paper 1, June 2025: Question 30

1 mark · Medium difficulty · Multiple Choice

Determine the expression for the Planck constant in terms of the intercepts of a graph of maximum kinetic energy against frequency for the photoelectric effect.

Practise this question

Question

A multiple-choice question showing a graph of maximum kinetic energy Ek(max) on the vertical axis against frequency f on the horizontal axis. The line has gradient p, an intercept of minus q on the Ek(max) axis, and an intercept of r on the frequency axis. Four options for the value of the Planck constant are provided: A: p/r, B: r/p, C: r/q, D: q/r.
Question text

30 In a photoelectric experiment, the maximum kinetic energy Ek(max) of the emitted electrons

and the frequency f of the incident radiation are measured.

A graph of the variation of Ek(max) with f has:

• a gradient p

• an intercept −q on the Ek(max) axis

• an intercept r on the f axis.

What is the value of the Planck constant?

[1 mark]

p

A

r

r

B

p

r

C

q

q

D

r

Mark scheme

Show the mark scheme Mark scheme table showing question number 30 with correct answer D (q/r), targeting assessment objective AO1.

q

30 D AO1

r

How to answer it

Photoelectric Effect: Graph Analysis & Planck's Constant

📌 What this question tests

This question assesses your ability to relate Einstein's photoelectric equation to the straight-line graph equation y = mx + c . Specifically, you must link the mathematical features of the graph (gradient, vertical intercept, and horizontal intercept) to physical quantities: Planck's constant ( h ), the work function ( Φ ), and the threshold frequency ( f₀ ).

Question 30 (Multiple Choice)

1 Mark • AO1 (Demonstrate knowledge and understanding)

✅ Correct Answer

D — q / r

Mark Scheme Breakdown:
1 mark for selecting option D.

💡 Key Knowledge

  • Photoelectric Equation:
    Ek(max) = hf − Φ
  • Straight-line equivalence ( y = mx + c ):
    • y -variable = Ek(max)
    • x -variable = f
    • Gradient m = h = p
    • y -intercept c = −Φ = −q ⇒ Work function Φ = q
    • x -intercept (y = 0) : hf₀ = Φ ⇒ Threshold frequency f₀ = r

📐 Step-by-Step Derivation

You need an expression for Planck's constant h in terms of the given graph parameters p , q , and r .

Method 1: Using the definition of gradient ( gradient = Δy / Δx )

  1. Identify two convenient points on the line:
    • Vertical intercept: (0, −q)
    • Horizontal intercept: (r, 0)
  2. Calculate the gradient of the line:
    gradient = (0 − (−q)) / (r − 0) = q / r
  3. From Einstein's photoelectric equation, the gradient equals the Planck constant:
    h = gradient = p = q / r

Method 2: Using the intercepts directly

  1. At the f -axis intercept, Ek(max) = 0 and f = r .
  2. Substitute into Ek(max) = hf − Φ :
    0 = h(r) − Φ ⇒ h = Φ / r
  3. The magnitude of the negative vertical intercept is the work function: Φ = q .
  4. Substitute Φ = q into the equation:
    h = q / r

🧠 Exam Technique

  • Check available options: Although h = p is true, p alone is not one of the choices. This immediately tells you to express p using the other geometric quantities of the graph.
  • Dimensional analysis shortcut:
    • q is an energy (J)
    • r is a frequency (s⁻¹ or Hz)
    • h = Energy / Frequency = J / s⁻¹ = J s
    • Therefore, h must have units of q / r , which instantly rules out A, B, and C!

❌ Common Errors

  • Inverting the ratio (choosing C — r / q): Inverting the gradient formula and doing Δx / Δy instead of Δy / Δx .
  • Confusing the gradient with an intercept (choosing A or B): Trying to divide the gradient p by r . Since p = q / r , the ratio p / r would equal h / f₀ , which is not equal to h .
  • Sign confusion with −q: Thinking the answer must be negative. Magnitudes are positive; the vertical intercept is at −q , so the work function Φ = +q .

Topics

Physics · Practical skills · 3.2 Particles and radiation · Data analysis

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.