The ratio of the total energy of the 2^ nd orbit electron for the hydrogen atom 1 H ^1 to that of helium ion ( He ⁺ ) 2 He ^4 is

Step-by-step solution

Total energy of an electron in a hydrogen-like atom: E_n = -13.6 Z^2 n^2 eV For hydrogen ( Z = 1 in the n = 2 orbit): E_ H,2 = -13.6 1^2 2^2 = -3.4 eV For helium ion He⁺ ( Z = 2 in the n = 2 orbit): E_ He,2 = -13.6 2^2 2^2 = -13.6 eV The energy ratio is E_ H,2 E_ He,2 = -3.4 -13.6 = 1 4