Question

An electron of mass $m$ and charge $e$ is accelerated from rest through a potential difference of $V$ volt in vacuum. Its final speed will be

• A. $\frac{eV}{2m}$
• B. $\frac{eV}{m}$
• C. $\sqrt{\frac{2eV}{m}}$
• D. $\sqrt{\frac{eV}{2m}}$

Answer 1

The correct option is C $\sqrt{\frac{2eV}{m}}$

• Energy gained by electron when accelerated through a potential $V$ is $charge\times voltage$ i.e., $eV$
• As Kinetic energy
• of any mass $m$ is given as $\frac{m{v}^2}{2}$
• so velocity $v$= $\sqrt[2]{2\frac{2K.E.}{m}}$
• for final speed put $K.E.=eV$ we get final speed $v$= $\sqrt[2]{2\frac{2eV}{m}}$. Option C is correct