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

Asked in JEE Main 3rd Sept 2nd Shift 2020 · Accelerated charges

Answer: (3) 2:1

Step-by-step solution

Both ions carry charge +e and start from rest, so the work-energy theorem gives eV=1/2mv².

Hence v=√(2eV)/m, i.e. v∝1/(√m) since e and V are the same for both.

(v_H)/(v_He)=√(m_He)/(m_H)=√4/1=2.

The ratio is 2:1.

Why the other options are wrong

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