Question

A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons ? 

(1) 6 

(2) 3 

(3) 10 

(4) 1

Answer 1

Correct option is :  (4) 1   

\( \because \ \mathrm{E} \propto \frac{\mathrm{z}^2}{\mathrm{n}^2} \) 

Energy of the \(2^{\text {nd }}\) orbit 

\( \begin{aligned} & =\frac{-13.6}{4}=-3.4 \mathrm{eV} \end{aligned} \) 

\( \begin{aligned} & \Delta \mathrm{E}_{2.1}=10.2 \mathrm{eV} \end{aligned} \)   

So, only possible transition is from 

\( \mathrm{n}=2 \text { to } \mathrm{n}=1 \)