A mass spectrometer is a device that uses a magnetic field to sort atoms by mass

Question

A mass spectrometer is a device that uses a magnetic field to sort atoms by mass. In this device, atoms whose masses are to be determined are ionized by stripping off one electron. They are then sent through a velocity selector (see problem E8M.2) that selects ions only with a very specific speed |v|, and these ions are sent into a region of space filed with a uniform magnetic field of known magnitude |B| that is perpendicular to v. The field causes the atom to follow a circular path. Atoms with different masses will follow somewhat different circular paths and thus end up at different places on a detector plate, as shown below. Argue that R m for ions with the same magnitude of charge and find the constant of proportionality. imagine that we give N^+ ions, O^+ ions, and NO^+ ions the same speed of 30.0 km/s and then send them into a mass spectrometer where |B| = 0.0500 T. How far would the spot on the photographic plate be from the entry point for each ion, assuming that each ion completes half an orbit, as shown in the figure? The atomic mass of a nitrogen atom is 14.0031 u and oxygen is 15.9949 u, where 1 u = 1 "atomic mass unit" = 1.6605 times 10^-27 kg.

Explanation / Answer

a)

For the circular motion, the magnetic force will provide the necessary centripetal force

So, mv^2/R = qvB

So, mv/qB = R

So, R = m*(v/qB)

So, R proportional to m with the constant of proportionality being = v/qB

b)

radius , R = mv/qB

For N+ ion, m = 14 amu = 14*1.66*10^-27 = 2.32*10^-26 kg

v = 30 km/s = 3*10^4 m/s

q = 1.6*10^-19 C

B = 0.05 T

So, R = 2.32*10^-26*3*10^4/(1.6*10^-19*0.05)

= 0.087 m

So, distance from entry point = 2R = 0.174 m

Now , for O+ ion,

m = 16 amu = 1.6*1.66*10^-27 kg

So, R = 16*1.66*10^-27*3*10^4/(1.6*10^-19*0.05)

= 0.0996 m

So, distance from the entry point = 2*R = 0.1996 m

and for NO+ ion:

m = 16 + 14 = 30 amu = 30*1.66*10^-27

So, R = 30*1.66*10^-27*3*10^4/(1.6*10^-19*0.05)

= 0.1868 m

So, distance from the entry point = 2R = 0.374 m

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