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

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(3) 1/(√2). Given: both ions start from rest and fall through the same potential difference V. Idea: the work done on the charge becomes kinetic energy, 1/2mv²=qV, so v=√(2qV)/m. A doubly ionised helium atom has q=2e and m=4m_H; a hydrogen ion has q=e and m=m_H. (v_He)/(v_H)=√(2e/4m_H)/(e/m_H)=√1/2. So the ratio is 1/(√2): the heavier helium ion ends up the slower of the two.

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

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