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 slit is d = 1.80 m.


Chlorine ions of mass 35 amu (1 amu equals 1.66×10-27 kg), carrying a charge of +1e enter the spectrometer with initial speed of vo = 5.90×105 m/s. What value of B is required for these ions to hit the detector?

The magnetic force is directed perpendicular to the velocity causing circular motion. Set the magnetic force equal to the mass times the centripetal acceleration. What should the radius of the circle be?

Equally charged chlorine ions of mass 37 amu now enter the spectrometer. How close to the detector slit will they impact?

Explanation / Answer

Part A.

Using force balance

Fm = Fc

qvB = mv^2/r

So

r = mv/qB

B = mv/qr

r = d/2 = 1.80/2 = 0.90 m

Using given values:

B = 35*1.67*10^-27*5.90*10^5/(1.6*10^-19*0.90)

B = 0.239 T

Part B

Now in this case

r = mv/qB

r = 37*1.67*10^-27*5.90*10^5/(1.6*10^-19*0.239)

r = 0.953 m

d = 1.906 m

difference between both will be = 1.906 - 1.80 = 0.106 m

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