Estimate the speed with which electron emitted from a heated cathode of an evacuated tube impinge on the anode maintained at a potential difference of $500\;v$ , with respect to the cathod . Ignore the small initial speeds of the electrons . The specific charge of the electron (ie) its $\large\frac{e}{m}$ is given to be $1.76 \times 10^{11}\;kg^{-1}$ use the same formula you employ to obtain electron speed for an anode potential of 10 Mv. Do you see what is wrong ? In what way in is the formula to be modified ?

Question

$\begin{array}{1 1} \frac{ev}{m_0 c^2} -1 = \frac{1}{\sqrt {1- \large\frac{u^2}{c^2}}} \\ \frac{ev}{m_0 c^2} -1 = \frac{1}{\sqrt {1- \large\frac{c^2}{u^2}}} \\ \frac{ev}{m_0 c^2} +1 = \frac{1}{\sqrt {1- \large\frac{c^2}{v^2}}} \\ \frac{ev}{m_0 c^2} + 1 = \frac{1}{\sqrt {1- \large\frac{v^2}{c^2}}}\end{array}$