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 × 1011 C kg−1.
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Solution
Potential difference across the evacuated tube, V = 500 V
Specific charge of an electron, e/m = 1.76 × 1011 C kg−1
The speed of each emitted electron is given by the relation for kinetic energy as:
`KE = 1/2 mv^2 = eV`
`:. v = ((2eV)/m)^(1/2) = (2V xx e/m)^(1/2)`
`= (2 xx 500 xx 1.76 xx 10^11)^(1/2) = 1.327 xx 10^ "m/s"`
Therefore, the speed of each emitted electron is `1.327 xx 10^7 "m/s"`
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