An electron in a certain Bohr orbit of a He ⁺ ion has the same energy as an electron in the first Bohr orbit of a hydrogen atom. The principal quantum number of this orbit for the He ⁺ ion is:

Step-by-step solution

The energy of an electron in the n^ th Bohr orbit of a hydrogen-like species is given by: E_n = -13.6 Z^2 n^2 eV For the first Bohr orbit of a hydrogen atom ( Z = 1, n = 1 ): E₁( H ) = -13.6 1^2 1^2 = -13.6 eV For the n^ th Bohr orbit of a He ⁺ ion ( Z = 2 ): E_n( He ⁺) = -13.6 2^2 n^2 = -13.6 4 n^2 eV Given that the energies are equal: -13.6 = -13.6 4 n^2 4 n^2 = 1 n^2 = 4 n = 2 Answer: 2