Q. Doubly ionised helium atom and hydrogen ions are accelerated, from rest, through the same potential difference. The ratio of final velocities of helium and hydrogen is
A) $1\ :\ \sqrt{2}$
B) $\sqrt{2}\ :1$
C) $1\ :2\ $
D) $2\ :1$
Explanation
(a) $qV = \frac{1}{2}mv^{2}\ or\ v = \frac{\sqrt{2qV}}{m}$
$ie,\ v = \frac{\sqrt{2qV}}{m}\ \ \therefore\ \frac{v_{He}}{v_{H}} = \sqrt{\frac{q_{He}}{q_{H}} \times \frac{m_{H}}{m_{He}}} = \sqrt{\frac{2e}{e} \times \frac{m}{4m}} = \frac{1}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.