This example problem demonstrates how to find the energy that corresponds to an energy level of a Bohr atom.
Problem:
What is the energy of an electron in the 𝑛=3 energy state of a hydrogen atom?
Solution:
E = hν = hc/λ
According to the Rydberg formula:
1/λ = R(Z2/n2) where
R = 1.097 x 107 m-1
Z = Atomic number of the atom (Z=1 for hydrogen)
Combine these formulas:
E = hcR(Z2/n2)
h = 6.626 x 10-34 J·s
c = 3 x 108 m/sec
R = 1.097 x 107 m-1
hcR = 6.626 x 10-34 J·s x 3 x 108 m/sec x 1.097 x 107 m-1
hcR = 2.18 x 10-18 J
E = 2.18 x 10-18 J(Z2/n2)
E = 2.18 x 10-18 J(12/32)
E = 2.18 x 10-18 J(1/9)
E = 2.42 x 10-19 J
Answer:
The energy of an electron in the n=3 energy state of a hydrogen atom is 2.42 x 10-19 J.