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.

Solution

Here,
Potential difference, V = 500 V
Specific charge on electron,

\frac{e}{m} = 1.76 \times 10^{11} C {kg}^{- 1}

kinetic energy is the work done on the electron by potential difference between the cathode and the anode.
Thus,

\frac{1}{2} {mv}^{2} = eV

\Rightarrow

v = \sqrt{\frac{2 eV}{m}} = \sqrt{2 \times 1.76 \times 10^{11} \times 500}

i.e.,

v = 1.327 \times 10^{7} {ms}^{- 1}

is the speed with which the electrons are getting impinged on the collector.

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