The radius of the second Bohr orbit, in terms of the Bohr radius, a₀, in Li²⁺ is :

Solution

Chemistry ma’am · 3 steps

Bohr radius grows as n² and shrinks as Z: put n = 2 and Z = 3 for Li²⁺.

1. Hydrogen-like ion. Li²⁺ has only one electron left, so Bohr's model applies to it just as it does to hydrogen. The only change is the nuclear charge, Z = 3.

   rₙ = n²/Z a₀

2. Put in numbers. For the second orbit n = 2, so n² = 4. Dividing by Z = 3 gives r₂ = 4/3a₀.
3. So. The radius of the second Bohr orbit of Li²⁺ is 4a₀/3, option (d).

The idea to keep. For any one-electron species, r ∝ n²/Z. Square the orbit number, but divide by Z only once. Energy goes as Z²/n², radius does not.

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