A mass spectrometer, sketched below, is a device used to separate different ions

Question

A mass spectrometer, sketched below, is a device used to separate different ions. Such ions with a well-defined velocity v_0 enter through a slit into a region of uniform magnetic field B, where they follow a semicircular path until they strike the detector slit above the entry slit. The distance between the entry and the detector slit is d = 1.50 m. Chlorine ions of mass 35 amu (1 amu equals 1.66 times 10^-27 kg), carrying a charge of + 1e enter the spectrometer with initial speed of v_0 = 5.10 times 10^5 m/s. What value of B is required for these ions to hit the detector? Equally charged chlorine ions of mass 37 amu now enter the spectrometer. How close to the detector slit will they impact?

Explanation / Answer

a) the magnetic force serves as the centripetal force
m v^2 / R = q v B

B = m v / (R q)

B = 35*1.66*10^-27*(5.1*10^5)/0.75*1.6*10^-19 = 0.247 T

b) d' / d = m' / m
d' = (m' / m) d
distance is d' - d = (m'/m - 1) d = (37/35-1) = 0.0857 m

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