Question

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the $n=4th$ level. Determine the wavelength and frequency of photon.

Answer 1

For ground level, $n_1=1$.

$E_1=-13.67/n_1^2=13.67eV$

The atom is excited to higher level, $n_2=4$.

$E_2=-13.67/n_2^2=13.67/16eV$

$E=E_1-E_2=hc/\lambda$

$\lambda =\frac{hc}{E_1-E_2}$

$\Rightarrow \frac{6.6\times {10}^{-34}\times 3\times {10}^8}{13.67-\frac{13.67}{16}}$

$\Rightarrow \lambda =97nm$

$c=\lambda \nu$

$\Rightarrow \nu =3.1\times {10}^{15}Hz$