Question

Doubly ionised Helium atoms and Hydrogen ions are accelerated from rest through the same potential drop. The ratio of the final velocities of the Helium and the Hydrogen ions is

• A. 2
• B. $\sqrt{2}$
• C. 1/2
• D. 1/$\sqrt{2}$

Answer 1

The correct option is D 1/$\sqrt{2}$

Mass of Hydrogen ion is $m_p$.
Mass of Helium ion $m_{He}=4m_p$
Charge of Hydrogen ion is $q_p$.
Charge of Helium ion $q_{He}=2q_p$
Kinetic energy of particle $K.E=\frac{1}{2}m{v}^2=qV$
$⟹v\propto \sqrt{\frac{q}{m}}$
We get $\frac{v_{He}}{v_H}=\sqrt{\frac{q_{He}}{m_{He}}.\frac{m_p}{q_p}}$
$⟹$ $\frac{v_{He}}{v_H}=\sqrt{\frac{2q_p}{4m_p}.\frac{m_p}{q_p}}=\frac{1}{\sqrt{2}}$