If the energy of an electron in the first Bohr orbit of a hydrogen atom is -E , then the energy of an electron in the third Bohr orbit of a 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 = -E₀ Z^2 n^2 . For a hydrogen atom ( Z=1 ) in the first Bohr orbit ( n=1 ), the energy is E₁( H ) = -E₀ 1^2 1^2 = -E . For a He ⁺ ion ( Z=2 ) in the third Bohr orbit ( n=3 ), the energy is E₃( He ⁺) = -E₀ 2^2 3^2 = -E₀ 4 9 . Substituting E₀ = E , we get E₃( He ⁺) = - 4 9 E . Answer: - 4 9 E