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

Explanation

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)-(E_0)/(4)=15 rArr (3E_0)/(4)=15`
`rArr E_(0)=20eV`
for `n=4,E_(4)=(E_0)/(16)`
Third excitation energy =
`E_(0)-(E_0)/(16)=-(15E_0)/(16)=(15xx20)/(16)=(75)/(4)eV`
THird potentials is `(75)/(4)eV`.