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 = 1.20 m.


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 = 8.70E5 meters/sec. 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

Given that mass of Chlorine is m=35 x 1.66 x 10-27 kg charge is q=1.6 x 10-19C speed is v=8.70 x 105 m/s distance d=1.20m hence the radius is r=0.6m if B is the magnetic field then mv2 /r=qvB B=mv/qr    = 0.5265T mass of Cl37 is m1=37 x 1.66 x 10-27 kg
r=mv/qB
=(37 x 1.66 x 10-27)(8.70 x 105 m/s)/(1.6 x 10-19C)(0.5265)
=0.63432 m
hence the distnace is d=1.268m
so the closest approach is 0.068m

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