Question

A photon of energy 12.4 eV is completely absorbed by a hydrogen atom initially in the ground state so that it is excited. The quantum number of the excited state is

• A. n = 1
• B. n = 3
• C. n = 4
• D. n = $\infty$

Answer 1

The correct option is C n = 4

Let electron absorbing the photon energy reaches to the excited state n. Then using energy conservation
$\Rightarrow -\frac{13.6}{n^2}=-13.6+12.4\Rightarrow -\frac{13.6}{n^2}=-1.2\Rightarrow n^2=\frac{13.6}{1.2}=12\Rightarrow n=3.46\simeq 4$