Question

Separation energy of a hydrogen like ion from its third excited state is 2.25 times the separation energy of
hydrogen atom from its first excited state. Final out the atomic number of hydrogen like ion.

Answer 1

Dear Student ,

Separation energy = $13.6\times \raisebox{1ex}{$z^2$}\!\left/ \!\raisebox{-1ex}{$n^2$}\right.$
so now for third excited state , n=4 so separation energy= $13.6\times \raisebox{1ex}{$z^2$}\!\left/ \!\raisebox{-1ex}{$4^2$}\right.=13.6\times z^2/16$
now separation energy for first excited state is given by =$13.6\times \raisebox{1ex}{$z^2$}\!\left/ \!\raisebox{-1ex}{$2^2$}\right.=13.6\times 1/4$
now $13.6\times z^2/16=2.25\times 13.6\times 1/4$
so z= 3

Regards,
Divyank