Bohr Atom Energy Level Example Problem

Finding Energy of an Electron in a Bohr Energy Level

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Helmenstine, Todd. "Bohr Atom Energy Level Example Problem." ThoughtCo, Feb. 8, 2017, thoughtco.com/bohr-atom-energy-level-problem-609463. Helmenstine, Todd. (2017, February 8). Bohr Atom Energy Level Example Problem. Retrieved from https://www.thoughtco.com/bohr-atom-energy-level-problem-609463 Helmenstine, Todd. "Bohr Atom Energy Level Example Problem." ThoughtCo. https://www.thoughtco.com/bohr-atom-energy-level-problem-609463 (accessed October 17, 2017).
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.