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in Physics by (52.3k points)

(a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the  emitter. Ignore the small initial speeds of, the electrons. The specific charge of the electron, i.e., its e/m is given to be 1.76 x 1011 C kg-1

(b) Use the same formula you employ in (a) to obtain electron speed for a collector potential of 10 MV. Do you see what is wrong? In what way is the formula to be modified?

1 Answer

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(a) V = 500 V
e/m = 1.76 × 1011 C kg-1
Due to the applied potential difference between the emitter and the collector, an emitted electron gains kinetic energy, which is given by

Using the same formula as in (a), the speed of electrons at 10 mV comes out to be greater than the speed of light. Since no material particle can move with the speed of light, the result is clearly wrong.

In fact, equation (1) is valid for kinetic energy of the electron, so long as V/C < < 1. At 10 mV, the electrons attain a speed comparable to the speed of light i.e. become relativistic.

In the relativistic domain:- The mass of the electron having rest mass m0 is

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