Considering the Bohr model of hydrogen like atoms, the ratio of the radius of 5ᵗʰ orbit of the electron in Li²⁺ and He⁺is

Solution

Physics sir · 4 steps

Same orbit number in both ions, so n² cancels and the radius ratio is just the inverse ratio of Z.

1. Bohr radius formula. For a hydrogen-like atom, the radius of the nth orbit grows as n² and shrinks as the nuclear charge Z grows.

   rₙ = 0.529 n²/Z Å

2. Cancel n. Both radii are for n = 5, so the n² factor cancels in the ratio. That leaves r_(Li²⁺)/r_(He⁺) = Z_(He)/Z_(Li).
3. Put in Z. Lithium has Z = 3 and helium has Z = 2. The ratio is 2/3, so the Li²⁺ orbit is smaller, as it should be: a larger nuclear charge pulls the electron in closer.
4. So. The ratio of the radii is 2/3, option (b).

The idea to keep. In Bohr's model, r ∝ n²/Z. More nuclear charge means a tighter orbit, so radius goes as the inverse of Z, not directly with it.

Answer from the NTA final answer key. Solution by PrepWiser.