# The wavelength of the photon emitted by a hydrogen atom when

Question:

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from $n=2$ to $n=1$ state is:

1. (1) $194.8 \mathrm{~nm}$

2. (2) $490.7 \mathrm{~mm}$

3. (3) $913.3 \mathrm{~nm}$

4. (4) $121.8 n m$

Correct Option: 4,

Solution:

(4)

$\Delta \mathrm{E}=10.2 \mathrm{eV}$

$\frac{\mathrm{he}}{\lambda}=10.2 \mathrm{ev}$

$\lambda=\frac{h c}{(10.2) e}$

$=\frac{12400}{10.2} \mathrm{~A}$

$=121.56 \mathrm{~nm}$

$\simeq 121.8 \mathrm{~nm}$