Calculate (i) First excitation energy of the electron in the hydrogen atom. (ii) Ionization energy of the hydrogen atom

Calculate (i) First excitation energy of the electron in the hydrogen

1.	Calculate (i) First excitation energy of the electron in the hydrogen atom. (ii) Ionization energy of the hydrogen atom
Answer» Solution :The energy of the ELECTRON in the nth shell of HYDROGEN atom is given by `E_(n) = - (2pi^(2) me^(4))/(n^(2) H^(2)) = - (1.312 xx 10^(6))/(n^(2)) J mol^(-1)` (i) First excitation energy is the amount of energy required to excite the electron from n = 1 (ground state) to n = 2 (first excited state) `Delta E = E_(2) - E_(1) = - (1.313 xx 10^(6))/(2^(2)) - (-(1.312 xx 10^(6))/(1^(2))) = - 3.28 xx 10^(5) + 13.12 xx 10^(5) J mol^(-1)` `= +9.84 xx 10^(5) J mol^(-1)` (ii) IONIZATION energy is the amount of energy required to REMOVE the electron from `n = 1 " to " n = oo`, i.e., `Delta E = E_(oo) - E_(1) (-1.312 xx 10^(6)) = +1.312 xx 10^(6) J mol^(-1)`