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,
Let be the energy of this level.
It is known that is related with as:
Step 2: Find the energy of the atom in the excited level.
The atom is excited to a higher level, = 4.
Let be the energy of this level.
Step 3: Find the wavelength and frequency of the photon.
For a photon of wavelength , the expression of energy is written as:
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