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In a mass spectrometer, ions are first accelerated through a potential difference V and then forced by a magnetic field B to move along a semicircular path of radius R. If V and B remain unchanged, how does the charge-to-mass ratio of the ion vary with R?

1. It is proportional to 1/R²
2. It is proportional to R²
3. It is proportional to R
4. It is proportional to 1/R

Correct answer: It is proportional to 1/R²

Solution

From qV = (1/2)mv^2 and R = mv/(qB): q/m = 2V/(R^2 B^2), so q/m is proportional to 1/R^2.

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