Chemistry

Problem

When the nuclear charge is increased from

+e

(hydrogen) to

+2e

(singly–ionized helium) and the electron occupies the lowest-energy orbit in each atom, how does the orbital speed of the electron change according to the Bohr model? a) It increases by a factor of

\sqrt{2}

. b) It remains the same. c) It increases by a factor of

2

. d) It decreases by a factor of

\dfrac{1}{2}

Intuitive explanation

In the Bohr model, the electron's orbital speed depends on the balance between the attractive nuclear force and the centripetal force needed to keep it in orbit. When nuclear charge doubles, the stronger pull draws the electron closer and accelerates it to maintain that tighter circular path. The key insight is that orbital speed scales directly with nuclear charge—so doubling $Z$ doubles the electron's speed, even though the orbit itself shrinks.

Intuitive explanation

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