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Convert Wavelength to Frequency 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 colors of the aurora derive from the emission spectra of ionized gases in the atmosphere.

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

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 wavelength of 5577 Å. What is the frequency of this light?

Solution:

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

Therefore

ν = c/λ

ν = 3 x 108 m/sec/(5577 Å x 10-10 m/1 Å)
ν = 3 x 108 m/sec/(5.577 x 10-7
ν = 5.38 x 1014 Hz

Answer:

The frequency of the 5577 Å light is ν = 5.38 x 1014 Hz.

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