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Convert Frequency to Wavelength Worked Example Problem

Spectroscopy Example Problem

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Aurora Borealis, or Northern Lights, above Bear Lake, Eielson Air Force Base, Alaska.

Aurora Borealis, or Northern Lights, above Bear Lake, Eielson Air Force Base, Alaska. The green color of the aurora derive from the emission spectra of ionized oxygen in the atmosphere.

United States Air Force photo by Senior Airman Joshua Strang
This example problem demonstrates how to find the wavelength of light from the frequency.

Problem:

The Aurora Borealis is a night display in the Northern latitudes caused by ionizing radiation interacting with the Earth's magnetic field and the upper atmosphere. The distinctive green color is caused by the interaction of the radiation with oxygen and has a frequency of 5.38 x 1014 Hz. What is the wavelength of this light?

Solution:

The speed of light, c, is equal to the product of the wavelength, &lamda;, and the frequency, ν.

Therefore

λ = c/ν

λ = 3 x 108 m/sec/(5.38 x 1014 Hz)
λ = 5.576 x 10-7 m

1 nm = 10-9 m
λ = 557.6 nm

Answer:

The wavelength of the green light is 5.576 x 10-7 m or 557.6 nm.

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