Bohr Atom Energy Level Example Problem

Finding Energy of an Electron in a Bohr Energy Level

Atomic structure
Atomic structure. Getty Images/MEHAU KULYK/SCIENCE PHOTO LIBRARY

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.