Radius of the first excited state of Helium ion is given as : a₀ → radius of first stationary state of hydrogen atom.

Solution

Chemistry ma’am · 4 steps

First excited state means n = 2, and for He⁺ Z = 2, so put both into r = a₀n²/Z.

1. Bohr radius formula. For a one-electron species, the radius of the nth orbit grows as n² and shrinks as the nuclear charge Z grows.

   rₙ = a₀ n²/Z

2. Pick n and Z. The ground state is n = 1, so the first excited state is n = 2. The helium ion He⁺ has Z = 2 and only one electron, so Bohr's model applies.
3. Put in numbers. r = a₀ × 2²/2 = a₀ × 4/2 = 2a₀.
4. So. The radius is 2a₀, which is option (b).

The idea to keep. Radius goes as n²/Z and energy goes as Z²/n². Do not mix up the two. Also remember that the first excited state is n = 2, not n = 1.

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