Question

(a) Estimate the speed with which electrons emitted from a heatedemitter of an evacuated tube impinge on the collector maintainedat a potential difference of 500 V with respect to the emitter.Ignore the small initial speeds of the electrons. Thespecific charge of the electron, i.e., its e/m is given to be1.76 × 1011 C kg–1. (b) Use the same formula you employ in (a) to obtain electron speedfor an collector potential of 10 MV. Do you see what is wrong ? Inwhat way is the formula to be modified?

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Solution

a)

Given: The potential difference between collector and emitter is

The work done on the electron by the potential difference is equal to the kinetic energy of the electron.

Where,

By substituting the values in the above equation, we get

Thus, the speed of the electron is

b)

The speed of the electron for potential difference

This value of speed is not possible because it is greater than the speed of light. The above formula is valid only for speed

When the speed of particle approaches to the speed of light, the mass of the particle starts to change according to the relation,

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