When an electron is accelerated through a high potential difference (V), then the mass of electron varies with its velocity. Hence, we have to consider its relativistic mass. Hence, we calculate its relativistic wavelength and total energy in the following way.
(a) Relativistic wavelength is calculated as follows:
The momentum of an electron is:
Divide Equation (4.8) by m0c, then:
Add and subtract 1 to the numerator,
Squaring and rearranging Equation (4.9),
The kinetic energy (E) of an electron is given by: ...