Question

The first excitation potential of a hypothetical hydrogen- like atom is `15 V`. Find the third excitation potential of the atom.

Answer 1

Let energy of ground state `=E_(0)`
`E_(0)= -13.6Z^(2)eV` and `E_(n)=(E_(0))/(n^(2))`
`n=2, E_(2)=(E_(0))/(4)`
given `(E_(0))/(4)-E_(0)=15`
`-(3E_(0))/(4)=15`
for `n=4, E_(4)=(E_(0))/(16)`
third exicitation energy `=(E_(0))/(16)-E_(0)`
`=-(15)/(16)E_(0)=-(15)/(16).((-4xx15)/(3))`
`=(75)/(4)eV`
`:.` third exclination potential is `(75)/(4)V`