The figure at right is a schematic diagram of a mass spectrometer, a device used

Question

The figure at right is a schematic diagram of a mass spectrometer, a device used in many scientific fields to measure the masses of ionized atoms and molecules to high precision and accuracy. An ion of mass M and charge tq is produced essentially at rest in the sample chamber S, in which a high-voltage arc or an electron beam produces ionized atoms The ion is accelerated by the potential difference V, and allowed to enter a magnetic field B. In the field it moves in a semicircle, striking a detector - commonly an ordinary CCD camera - at distance x from the entry slit and being recorded. Show that the mass M is given by B2 8V

Explanation / Answer

to find speed of charge after accelerating through potential V.

M v^2 / 2 = q V

v = sqrt[ 2 q V / M]

For circular path in magnetic field,

q v B = M v^2 / r

r = x/2

q B = 2 M v / x

q^2 B^2 = 4 M^2 (2 q V / M) / x^2

q B^2 = 8 M V / x^2

M = q B^2 x^2 / 8 V

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