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(Z^{2}/n^{2}) where

R = 1.097 x 10^{7} m^{-1}

Z = Atomic number of the atom (Z=1 for hydrogen)

Combine these formulas:

E = hcR(Z^{2}/n^{2})

h = 6.626 x 10^{-34} J·s

c = 3 x 10^{8} m/sec

R = 1.097 x 10^{7} m^{-1}

hcR = 6.626 x 10^{-34} J·s x 3 x 10^{8} m/sec x 1.097 x 10^{7} m^{-1}

hcR = 2.18 x 10^{-18} J

E = 2.18 x 10^{-18} J(Z^{2}/n^{2})

E = 2.18 x 10^{-18} J(1^{2}/3^{2})

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.