With the increase in peinciple quantum number, the energy difference between the two successive energy levels

Options

A. decrease
B. increase
C. first decrease and then increase
D. remain the same

Answer

A

Explanation

Total energy for nth level `= - (13.6)/(n^(2)) eV`
`E_(2) - E_(1) = - 13.6 ((1)/(4) - (1)/(1))`
`= (13.6 xx 3)/(4) = 0.75 xx 13.6 eV`
`E_(3) - E_(2) = - 13.6 ((1)/(9) - (1)/(4))`
`= (13.6 xx 5)/(36) = 0.14 xx 13.6 eV`
`E_(4) - E_(3) = - 13.6 ((1)/(16) - (1)/(9))`
`= (13.6 xx 7)/(144) eV = 0.05 xx 13.6 eV`
Obvionusly, the different of energy between consecutive energy levels decrease.