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 vo 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 slits is d = 1.30 m.

Chlorine ions of mass 35 amu , carrying a charge of +1e, enter the spectrometer with initial speed of vo = 9.40E5 meters/sec. What value of B is required for these ions to hit the detector?

Explanation / Answer

First we convert amu into kg so-

35 amu = 5.812*10-26 Kg

d = 2r = 1.30m

r = 0.65 m

Now we that for complete the semicircular path to hitting the detector-

r = mv/qB

so-

B = mv/qr

B = 5.812*10-26 * (9.40 * 105) / (1.6*10-19) (0.65)

B = 54.633 * 10-21 / (1.048 *10-19 )

B = 52.1307 * 102 T

B = 5213.07 T

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