If the radius of the third Bohr orbit of a hydrogen atom is R , then the radius of the second Bohr orbit of a Be³⁺ ion will be:

Step-by-step solution

The radius of the n -th Bohr orbit for a hydrogen-like species is given by r_n = r₀ n^2 Z , where r₀ is the Bohr radius. For the third Bohr orbit of a hydrogen atom ( n = 3, Z = 1 ): R = r₀ 3^2 1 = 9 r₀ r₀ = R 9 For the second Bohr orbit of a Be³⁺ ion ( n = 2, Z = 4 ): r' = r₀ 2^2 4 = r₀ 4 4 = r₀ Substituting the value of r₀ , we get: r' = R 9 Answer: R 9