First we find for the wavelength of the photon released due to change in energy level. We use the Rydberg equation:
1/ʎ = R [1/n1^2 – 1/n2^2]
where,
ʎ is the wavelength
R is the rydbergs constant = 1.097×10^7 m^-1
n1 is the 1st energy level = 1
n2 is the higher energy level = infinity, so 1/n2 = 0
Calculating for ʎ:
1/ʎ = 1.097×10^7 m^-1 * [1/1^2 – 0]
ʎ = 9.1158 x 10^-8 m
Then calculate the energy using Plancks equation:
E = hc/ʎ
where,
h is plancks constant = 6.626×10^−34 J s
c is speed of light = 3x10^8 m/s
E = (6.626×10^−34 J s * 3x10^8 m/s) / 9.1158 x 10^-8 m
E = 2.18 x 10^-18 J = 2.18 x 10^-21 kJ
This is still per atom, so multiply by Avogadros number = 6.022 x 10^23 atoms / mol:
E = (2.18 x 10^-21 kJ / atom) * (6.022 x 10^23 atoms / mol)
E = 1312 kJ/mol
