J. J. Thomson is best known for his discoveries about the nature of cathode rays

Question

J. J. Thomson is best known for his discoveries about the nature of cathode rays. His other important contribution was the invention, together with one of his students, of the mass spectrometer, a device that measures the ratio of mass m to (positive) charge q of an ion.

The spectrometer consists of two regions as shown in the figure.(Figure 1) In the first region an electric field accelerates the ion and in the second the ion follows a circular arc in a magnetic field. The radius of curvature of the arc can be measured and then the m/q ratio can be found.

Part A

After being accelerated to a speed of 1.56

Explanation / Answer

Let m = mass of particle, q = charge, v = speed, B = magentic field strength, r = radisu of curvature.

The particle is subject to force due to the magnetic field:

F = qvB

Which is balanced by a centripital force

Fc = mv^2/r

So equating the two:

F = Fc ---> qvB = mv^2/r ---> re-arrange to get m/q

m/q = rB/v = 0.34 m* 0.7T/1.56x10^5 m/s = 1.52x10^-6 kg/C

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