Question

An electron initially at rest, is accelerated through a potential difference of $200V$, so that it acquires a velocity of $8.4\times {10}^{6}m/s$ . The value of $e/m$ of electron will be :

• A. $2.76\times {10}^{12}C/kg$
• B. $1.76\times {10}^{11}C/kg$
• C. $0.76\times {10}^{12}C/kg$
• D. none of these

Answer 1

Answer: (B)

Energy acquired due to potential difference gives the kinetic energy.
Energy acquired by electron of charge $e$ due to potential $V$
$E=eV$ This provides kinetic energy to the electron,
i .e, $E=eV=\frac{1}{2}m{v}^2$
where $m$ is mass. The ratio $\frac{e}{m}$ is given by
$\frac{e}{m}=\frac{v^2}{2V}$
Given, $v=8.4\times {10}^{6}m/s,V=200$ volt
$\therefore$ $\frac{e}{m}=\frac{{(8.4\times {10}^6)}^2}{2\times 200}$
$=1.76\times {10}^{11}C/kg$ .
Note: The ratio $e$- is known as specific charge.