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)`, then
`E_(n) = - E_(0)/( n^(2))`
given `E_(2) - E_(1)15 e V implies implies - (E_(0))/(4) + E_(0) = 15 implies (3 E_(0))/(4) = 15`
`implies c= 20 e V`
For the third excitation potential : `n = 4`, then
`E_(4) - E_(1) = - (E_(0))/(16) + E_(0) = (75)/(4) e V`
Therefore, the third potential is `(75//4) V`