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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 ion is

1. 1/2
2. 2
3. 1/√2
4. √2

Correct answer: 1/√2

Solution

The kinetic energy gained by a charged particle accelerated through a potential difference is equal to the charge multiplied by the potential difference. Since the charge of the helium ion is twice that of the hydrogen ion, but the mass of the helium ion is four times that of the hydrogen ion, the velocity ratio is determined by the square root of the charge-to-mass ratio. This gives a ratio of 1/√2.

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