Question

Electrons of energies $10.20eV$ and $12.09eV$ can cause radiation to be emitted from hydrogen atoms. Calculate, in each case, the principal quantum of the orbit to which electron in the hydrogen atom is raised and the wavelength of the radiation emitted if it drops back to the ground state. Find the sum of these numbers.

Answer 1

$E=10.2eV$
$10.2=13.6(1-\frac{1}{n^2})$
$\Rightarrow n=2$
And for $E=12.09eV$
$12.09=13.6(1-\frac{1}{n^2})$
$n^2=9$
$n=3$
Sum of numbers $=3+2=5$