Hydrogen ion and 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 :

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2 : 1

10 : 7

1 : 2

5 : 7

answer is B.

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Detailed Solution

$\begin{array}{l} G a i n i n K i n e t i c e n e r g y = L o s s i n p o t e n t i a l e n e r g y \\ \Rightarrow \frac{1}{2} {mv}^{2} = q Δ V \\ \Rightarrow v = \sqrt{\frac{2 q Δ v}{m}} \\ \Rightarrow v \propto \sqrt{\frac{q}{m}} \Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{q_{1} m_{2}}{q_{2} m_{1}}} \Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{(q) 4 m}{qm}} \\ ∴ \frac{v_{1}}{v_{2}} = \frac{2}{1} \end{array}$

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