Explain how a mass spectrometer uses electric and magnetic fields to separate ions of the same charge but different mass, and explain why heavier ions are deflected less than lighter ions when travelling at the same speed through the magnetic field region.

IB DP Physics Higher Level (2023 syllabus) — D.3 Motion in electromagnetic fields · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

In a simple mass spectrometer, ions are accelerated through a potential difference before entering a region of uniform magnetic field directed perpendicular to their velocity.

Model answer (4 marks)

1. Ions are accelerated through a potential difference, gaining kinetic energy KE = qV and a speed v = \sqrt{2qV/m}. 2. They then enter a uniform magnetic field B perpendicular to their velocity. 3. The magnetic force F = qvB is always perpendicular to the velocity, so it provides the centripetal force m v²/r, giving r = mv/(qB). 4. For ions of the same charge and speed, a larger mass m gives a larger radius r, so heavier ions follow a wider, less curved path and are deflected less than lighter ions.

Examiner tips

  • Use the formula r = mv/(qB) to link mass and radius; mention that q and v are constant for the comparison.
  • Explain that the magnetic force is unchanged while the required centripetal force increases with mass, leading to a larger radius.

Common mistakes

  • Confusing the electric field with the magnetic field; forgetting that the electric field only accelerates the ions.
  • Assuming the magnetic force changes with mass; not recognising that qvB is independent of m for a given ion speed.

Mark scheme (4 marks)

  1. The electric field (potential difference) accelerates ions, giving them kinetic energy / speed before they enter the magnetic field region.
  2. The magnetic field exerts a force perpendicular to the ion's velocity, causing the ion to follow a circular path.
  3. The radius of the circular path is given by r = mv / (qB); for the same charge, speed, and field, a greater mass gives a greater radius.
  4. Heavier ions are deflected less (travel in a larger-radius arc) because a greater mass requires a larger centripetal force for the same circular acceleration, but the magnetic force qvB is unchanged, so the curvature is smaller.

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