AQA A-Level Physics Paper 1, November 2020: Question 13

1 mark · Medium difficulty · Multiple Choice

Identify which graph shows the variation of momentum with wavelength of a photon.

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Question

Multiple choice question 13 asking which graph shows the variation of momentum p with wavelength lambda of a photon, accompanied by four options labelled A, B, C, and D. Graph A shows an inverse proportionality curve starting high on the y-axis and decreasing asymptotically toward the x-axis. Graph B shows a similar decreasing curve but intersecting the y-axis at a lower point and with an asymptote above zero. Graph C shows a straight line with a negative gradient. Graph D shows a straight line with a positive gradient starting from the origin.
Question text

13 Which graph shows the variation of momentum p with wavelength λ of a photon?

[1 mark]

A B

C D

A

B

C

D

Mark scheme

Show the mark scheme The mark scheme table indicates the correct answer for question 13 is A.

13 A

How to answer it

Photon Momentum and Wavelength Graph

AQA A-Level Physics • Particles and Radiation • Multiple Choice

What this question tests

This question assesses your understanding of de Broglie wavelength and photon momentum relationships, specifically the inverse proportionality between momentum ( p ) and wavelength ( λ ), and your ability to interpret graphical representations of mathematical functions.

Question 13

Exam Part: Multiple Choice [1 mark]

Which graph shows the variation of momentum p with wavelength λ of a photon?

✅ Correct Answer: A

Graph A correctly shows a non-linear inverse proportionality curve where momentum approaches infinity as wavelength approaches zero, and approaches zero as wavelength becomes extremely large. Crucially, the curve never touches or crosses either axis.

💡 Key Knowledge

  • The momentum of a photon is given by the de Broglie equation: p = h / λ (where h is the Planck constant).
  • Since h is a constant, p is inversely proportional to λ ( p ∝ 1 / λ ).
  • Mathematically, this represents a rectangular hyperbola in the first quadrant.

🧠 Exam Technique

  • Test limits: As λ → 0 , p → ∞ (the line must shoot up infinitely high along the vertical axis). As λ → ∞ , p → 0 (the line must flatten out towards the horizontal axis).
  • Eliminate linear graphs immediately since the relationship is not y = mx + c .

❌ Common Errors

  • Choosing Graph B: Students often fail to notice whether curves touch the axes. Graph B shows a curve that intercepts the y-axis at a non-zero value or has an offset, which would imply a photon can have wavelength-independent momentum or non-zero momentum at infinite wavelength.
  • Choosing Graph C or D: Mistaking an inverse relationship for a linear negative correlation (C) or a direct proportionality (D).

Topics

Physics · 3.2 Particles and radiation

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, November 2020. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.