Comparing non-relativistic and relativistic calculation:

Relativistic calculation of the acceleration and motion in an electron gun

acceleration voltage Va
Non-relativistic computation of the electrons speed with ${v_{\text{non-rel}}=\sqrt{2\cdot \frac{e}{m}\cdot V_{\text a}}}$
${v_{\text {klas}}=0}$ $\frac{\text m}{\text s}$ ${v_{\text {rel}}=0}$ $\frac{\text m}{\text s}$
Relativistic computation of the electrons speed with ${v_{\text{relativistic}}=c\cdot \sqrt{1-\frac{1}{\left({1+\frac{V_{\text a}\cdot e}{m_{e}\cdot c^2}}\right)^2}}}$