Question

Electrons of energy 12.09 eV can excite hydrogen atoms. To which orbit is the electron in the hydrogen atom raised and what are the wavelengths of the radiations emitted as it drops back to the ground state?

Answer 1

Initial state is $1$ and let final state be $n_2$

$E=13.6\times z^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})12.09=13.6(1-\frac{1}{n_2^2})\Rightarrow n_2=3$

$R_H$=Rydberg constant

$\frac{1}{R_H}=912A^{\bullet }\frac{1}{\lambda }=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2}){\lambda }_{3\to 1}=\frac{9}{8R_H}=1026A^{\bullet }{\lambda }_{3\to 2}=\frac{36}{5R_H}=6,566.4A^{\bullet }$