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

Hint: Energy recieved by the hydrogen atom equals to the energy difference between the levels.
Step 1: Find the energy of the atom in the ground level.
For ground level, ${\mathrm{n}}_{1}=1$
Let ${\mathrm{E}}_{1}$ be the energy of this level.
It is known that ${\mathrm{E}}_{1}$ is related with ${\mathrm{n}}_{1}$ as:
$\begin{array}{rl}{E}_{1}& =\frac{-13.6}{{n}_{1}^{2}}\mathrm{eV}\\ & =\frac{-13.6}{{1}^{2}}=-13.6\mathrm{eV}\end{array}$
Step 2: Find the energy of the atom in the excited level.
The atom is excited to a higher level, ${\mathrm{n}}_{2}$ = 4.
Let ${\mathrm{E}}_{2}$ be the energy of this level.
Step 3: Find the wavelength and frequency of the photon.
For a photon of wavelength $\mathrm{\lambda }$, the expression of energy is written as:
$E=\frac{hc}{\lambda }$
where,
h=planck's constant
And, the frequency of a photon is given by the relation,
$$\nu=\frac{c}{\lambda}=\frac{3 \times 10^{8}}{9.74 \times 10^{-8}} \approx 3.1 \times 10^{15} \mathrm{~Hz}$$
Hence, the wavelength of the photone is 97.4 nm while the frequency is