Using the Bohr model for hydrogen-like atoms, the ratio of the radius of the 5th orbit in Li²⁺ to that in He⁺ is:
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Question

Using the Bohr model for hydrogen-like atoms, the ratio of the radius of the 5th orbit in Li²⁺ to that in He⁺ is:

G1 Physics · Accepted Answer

For a hydrogen-like ion, rₙ = a₀n²/Z. Both ions are considered in the same orbit n = 5, so n² cancels in the ratio: r(Li²⁺)/r(He⁺) = Z(He⁺)/Z(Li²⁺). For He⁺, Z = 2. For Li²⁺, Z = 3. Therefore, r(Li²⁺)/r(He⁺) = 2/3. Correct option: D.