First slide

Electrostatic potential energy

Question

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 :

Moderate

A

5 : 7
B

2 : 1
C

10 : 7
D

1 : 2

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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