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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# In the redshift of radiation from a distant galaxy, certain radiation, known to have a wavelength of 434 nm when observed in the laboratory, has a wavelength of 462 nm. (a) What is the radial speed of the galaxy relative to Earth? (b) Is the galaxy approaching or receding from Earth?

(a) The radial speed of the galaxy is 0.062c or .

(b) The observed wavelength is longer than the proper wavelength; hence, the galaxy is receding from us.

See the step by step solution

## Step 1: Doppler effect

(a)

In astronomy applications, the velocities of galaxies are estimated using Doppler shifts. Doppler shift is the difference between the observed and proper wavelength of light. The wavelength measured in the rest frame of the source is called proper wavelength . And the detected wavelength is related to the proper wavelength as

Where, is the speed parameter.

Inserting the given values in the above equations

Hence the radial velocity of the galaxy is 0.062c or .

## Step 2: Redshift or blue shift.

(b)

If the observed wavelength is longer than the proper wavelength, it implies that the galaxy is moving away from us and is said to be red-shifted.

If the observed wavelength is shorter than the proper wavelength, it implies that the galaxy is moving toward us and is said to be blue-shifted.

Here, the observed wavelength is longer than the proper wavelength; hence, the galaxy is receding from us.