Show that ground state energy of electron in hydrogen atom is equal to the first excited state energy of electron in He^(+) ion, assuming that their Rydberg's constants are equal

Show that ground state energy of electron in hydrogen atom is equal to

1.	Show that ground state energy of electron in hydrogen atom is equal to the first excited state energy of electron in He^(+) ion, assuming that their Rydberg's constants are equal
Answer» SOLUTION :`E_(n) = - R_(H) (Z^(2))/(n^(2)) = - 13.60 (Z^(2))/(n^(2)) eV` For H-atom in the ground state, `Z = 1, n =1, :. E_(1) = -13.60eV` For `He^(+)` ion in the first EXCITED state, `Z = 2, n = 2, E_(2) = - 13.60 xx (2^(2))/(2^(2)) = - 13.6 eV` HENCE, the desired result is proved.