Question

An electron is accelerated through a potential difference of $200V$. If e/m for the electron be $1.6\times {10}^{11}$ coulomb $k{g}^{-1}$, then the velocity acquired by the electron will be

• A. $8\times {10}^{6}m{s}^{-1}$
• B. $8\times {10}^{5}m{s}^{-1}$
• C. $5.9\times {10}^{6}m{s}^{-1}$
• D. $5.9\times {10}^{5}m{s}^{-1}$

Answer 1

The correct option is A $8\times {10}^{6}m{s}^{-1}$

Given : $\frac{e}{m}=1.6\times {10}^{11}C/kg$
Potential difference $V=200V$
Kinetic energy of electron $K.E=\frac{1}{2}m{v}^2=eV$
$\therefore$ $\frac{1}{2}m{v}^2=200e$
Or $v^2=\frac{400e}{m}=400\times 1.6\times {10}^{11}=64\times {10}^{12}$
$⟹v=8\times {10}^{6}m/s$