Question

An electron initially at rest, is accelerated through a potential difference of $200 \,V$, 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}}}{2\,V} $
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.