In a mass spectrometer, ions are first accelerated through a potential difference V, then describe semicircular paths of radius R in a magnetic field B. What is the mass of an ion in terms of its charge q?
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Question

In a mass spectrometer, ions are first accelerated through a potential difference V, then describe semicircular paths of radius R in a magnetic field B. What is the mass of an ion in terms of its charge q?

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G1 Physics · Accepted Answer

Step 1: Acceleration from rest through V provides kinetic energy qV = (1/2)mv². Step 2: Magnetic force supplies centripetal force: qvB = mv²/R. Step 3: Thus v = qBR/m. Insert this into the energy equation: qV = (1/2)m(q²B²R²/m²). Step 4: Rearranging gives m = qB²R²/(2V). Final answer: (A) qB²R²/(2V).