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 a detector slit a distance d above the entry slit. The distance between the entry and the detector slits is d = 1.90m.

Chlorine ions of mass 35 amu (1 amu equals 1.66x10-27 kg), carrying a charge of +1e, enter the spectrometer with initial speed of vo = 5.50E5 meters/sec. What value of B is required for these ions to hit the detector?

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 a detector slit a distance d above the entry slit. The distance between the entry and the detector slits is d = 1.90m. Chlorine ions of mass 35 amu (1 amu equals 1.66x10-27 kg), carrying a charge of +1e, enter the spectrometer with initial speed of vo = 5.50E5 meters/sec. What value of B is required for these ions to hit the detector?

Explanation / Answer

Here ,

as d = 1.90 m

r = d/2 = 0.95 m

Now , as r = mv/B*q

0.95 = 35*1.66*10^-27*5.5 *10^5 /(e*B)

B = 0.21 T

the magnetic field required is 0.21 T

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