Question

22. The ground state energy of hydrogen atom is -136
eV. When its electron is in the first excited state
its excitation energy is [AIPMT (Prelims)-2008)
(1) Zero
(2) 3.4 eV
(3) 6.8 eV
(4) 10.2 eV​

Answer 1

The answer is (4) 10.2eV

we know that,  Energy of nth shell =  -13.6$\frac{1}{n^{2} }$ eV       .....(I)

So, energy of first shell(ground state) = -13.6eV           ......(II)

and first exitation state means electron is in 2nd shell

thus using (I),

energy of 2nd shell = -3.4eV     .....(III)

Now,  Exitation energy for nth shell =  (Energy of final shell - energy of initial shell)

thus the required exitation energy is =  (III) - (II) = [-3.4 -(-113.6)]eV = 10.2eV