An electron occupies the fourth Bohr orbit of hydrogen, while another electron occupies the fourth Bohr orbit of He⁺. What is the ratio of the hydrogen-orbit radius to the He⁺-orbit radius?
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Question

An electron occupies the fourth Bohr orbit of hydrogen, while another electron occupies the fourth Bohr orbit of He⁺. What is the ratio of the hydrogen-orbit radius to the He⁺-orbit radius?

G1 Physics · Accepted Answer

For a hydrogen-like species, rₙ = a₀n² ÷ Z. Both electrons have the same n = 4, so radius varies only as 1 ÷ Z. For hydrogen, Z = 1. For He⁺, Z = 2. Therefore, r(H) ÷ r(He⁺) = 2. Hence the ratio is 2:1. Correct option: B.