# 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

> 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.

## 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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