Determine the first excitation potential for a He ^+ ion.

Step-by-step solution

The energy of an electron in the n -th orbit of a hydrogen-like ion is given by: E_n = -13.6 Z^2 n^2 eV For a He ^+ ion, the atomic number Z = 2 . The energy in the ground state ( n = 1 ) is: E₁ = -13.6 2^2 1^2 = -54.4 eV The energy in the first excited state ( n = 2 ) is: E₂ = -13.6 2^2 2^2 = -13.6 eV The first excitation energy is the energy required to excite the electron from n = 1 to n = 2 : E = E₂ - E₁ = -13.6 - (-54.4) = 40.8 eV The first excitation potential is the potential difference required to provide t