Question

An electron in the ground state of Hydrogen atom goes to an excited state by absorbing $12.1$ eV energy. In the course of it's transition to lower energy states, the possible number of spectral lines will be

• A. 1
• B. 3
• C. 6
• D. 10

Answer 1

Answer: (B)

Let electron rises to $E_{n}$ state by absorbing $12.1 eV$
$E_{1}-E_{n} =12.1 \,eV $
$-13.6-E_{n} =12.1$
$ E_{n} =-13.6-12.1=-1.5 $
since $E_{n}=-\frac{13.6}{n^{2}},-\frac{13.6}{n^{2}} =-1.5 $
$ n^{2} =\frac{13.6}{1.5}=9$
$ \therefore n =3 $
i.e., electron rises to $n=3$ state.
The number of possible spectral lines emitted during its transmission to ground state is $\frac{n(n-1)}{2}=3$