AQA A-Level Physics Paper 2, June 2023: Question 21

1 mark · Medium difficulty · Multiple Choice

Identify which statement correctly describes the motion of two isotopes with the same charge and speed moving in a uniform magnetic field.

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Question

Question 21: A beam consists of ionised atoms of two isotopes of an element. When the beam enters a uniform magnetic field, the ions move in circular paths. The ions have the same charge and travel at the same speed when they enter the magnetic field. Four multiple choice options are presented: A) The force acting on an ion is different for each isotope, B) The radius of the path followed by an ion is different for each isotope, C) The kinetic energy of an ion increases for both isotopes, D) The acceleration of an ion is the same for both isotopes.
Question text

21 A beam consists of ionised atoms of two isotopes of an element.

When the beam enters a uniform magnetic field, the ions move in circular paths.

The ions have the same charge and travel at the same speed when they enter the

magnetic field.

Which statement is true?

[1 mark]

A The force acting on an ion is different for each isotope.

B The radius of the path followed by an ion is different for each isotope.

C The kinetic energy of an ion increases for both isotopes.

D The acceleration of an ion is the same for both isotopes.

Mark scheme

Show the mark scheme Mark scheme for Question 21, indicating that the correct answer is option B: 'The radius of the path followed by an ion is different for each isotope.'

21 B The radius of the path followed by an ion is different for each isotope.

How to answer it

Motion of Isotopes in a Uniform Magnetic Field

📋 What This Question Tests

This question assesses your understanding of charged particles moving through uniform magnetic fields, specifically the physics of mass spectrometry. Key concepts tested include the magnetic force on moving charges ( F = BQv ), centripetal acceleration and force ( F = mv² / r ), orbital radius ( r = mv / (BQ) ), work done by magnetic forces, and how isotope mass affects motion.

Multiple Choice • Question 21

Analysis & Deductions

Evaluating the options step-by-step [1 Mark]

✅ Correct Answer: Option B

"The radius of the path followed by an ion is different for each isotope."

  • Centripetal force is provided by the magnetic force: BQv = mv² / r
  • Rearranging gives the orbital radius: r = mv / (BQ)
  • Both isotopes have identical charge ( Q ), identical speed ( v ), and are in the same field ( B ).
  • However, isotopes have different masses ( m ) due to different neutron numbers.
  • Since r ∝ m , the isotope with greater mass follows a path with a larger radius.

💡 Key Knowledge

  • Magnetic Force: F = BQv (acts perpendicular to velocity, so no work is done; kinetic energy and speed remain constant).
  • Circular Motion: r = mv / (BQ) and centripetal acceleration a = v² / r = BQv / m .
  • Definition of Isotopes: Atoms of the same element with the same number of protons (same charge when ionised to the same degree) but different numbers of neutrons (different mass).

📐 Step-by-Step Evaluation of Distractors

  1. Option A is FALSE:
    F = BQv . Since B , Q , and v are identical for both ions, the magnetic force acting on each ion is identical.
  2. Option C is FALSE:
    Magnetic force acts strictly at 90° to velocity ( W = F·d·cos(90°) = 0 ). No work is done on the ions, so speed and kinetic energy remain constant.
  3. Option D is FALSE:
    Acceleration is a = F / m = BQv / m . Because mass m is different for each isotope, the acceleration is different.

🧠 Exam Technique & Examiner Insight

  • Isolate the variable: Immediately identify what makes isotopes different: only mass.
  • Check invariance: If a formula does not contain mass m (such as F = BQv ), that quantity must be identical for both isotopes.
  • Remember work done in magnetic fields: A frequent examiner trap is suggesting magnetic fields alter particle kinetic energy. Unless an electric field is also present, a purely magnetic field never changes the speed or kinetic energy of a free charged particle.

❌ Common Errors & Pitfalls

  • Confusing Force and Acceleration: Students often assume that because the mass differs, the magnetic force must differ. Remember: F = BQv does not depend on mass! Only acceleration depends on mass ( a = F / m ).
  • Misunderstanding Work Done: Thinking circular motion causes acceleration in the direction of motion; it only causes centripetal acceleration changing direction, keeping Ek = ½mv² strictly constant.
  • Forgetting the Mass Spectrometer principle: This setup is the operational principle of a mass spectrometer—ions separate in radius solely based on their mass-to-charge ratio ( m/Q ).
Mark Scheme Reference: Question 21 • Answer: B (1 mark). No partial credit.

Topics

Physics · 3.2 Particles and radiation · 3.7 Fields and their consequences (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.