Question

Electrons of mass m and charge e are accelerated through a potential difference V and strike the target. The maximum speed of these electrons is

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

Answer 1

Answer: (D)

$\sqrt{\frac{2eV}{m}}$

Energy gained by the electron when accelerated through a potential of V volts.
$E=eV$
This energy is completely converted to kinetic energy:

$E=\frac{1}{2}m{v}^2$

Hence $\frac{1}{2}m{v}^2=eV$

$v^2=\frac{2eV}{m}$

And hence velocity of the electron is:

$v=\sqrt{\frac{2eV}{m}}$