Question

A hydrogen ion and a singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

• A. $1:2$
• B. $10:7$
• C. $2:1$
• D. $5:7$

Answer 1

The correct option is C $2:1$

According to work energy theorem,

The net work done will be equal to the change in kinetic energy.

$\therefore q\Delta V=\frac{1}{2}m{v}^2-0$

Here, $\Delta V=$ potential difference between two positions of charge $q$.

As the hydrogen ion and singly ionized helium atom has the same $q$ and given that $\Delta V$ is same,

$v\propto \frac{1}{\sqrt{m}}$

$\text{If the Mass of hydrogen ion,}{m}_{\text{H}}=m$
$\text{Then, Mass of helium ion}{m}_{\text{He}}=4m$

$\therefore \frac{v_H}{v_{He}}=\sqrt{\frac{4}{1}}=\frac{2}{1}.$

Hence, option $\left(C\right)$ is correct.