The ionization energy of a hydrogen-like ion in its first excited state is 30.6 eV . The energy required to excite the electron from the ground state to the first excited state in this ion is: (Given Rch = 13.6 eV )

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 The ionization energy from a given state is the energy required to remove the electron from that state to infinity ( n = ). For the first excited state ( n = 2 ), the ionization energy is: E_ - E₂ = 0 - ( - 13.6 Z^2 2^2 ) = 13.6 Z^2 4 = 3.4 Z^2 eV Given that the ionization energy in the first excited state is 30.6 eV : 3.4 Z^2 = 30.6 Z^2 = 30.6 3.4 = 9 The energy required to excite the electron from the ground s