Question

suppose a star is moving away from the earth at 75000 meters per second. you observe a line in the spectrum of the star which in laboratories on earth is at 500 nm. what will be the doppler shift (the change in wavelength δλ) of this line caused by the motion of the star? give your answer in nanometers. (to be clear, you are entering in the change in wavelength of the line, not the new wavelength.)
δλ = nm

Explanation:

Step1: Use the Doppler effect formula for light

The formula for the Doppler shift when the source (star) is moving away is \(\Delta\lambda=\lambda_0\frac{v}{c}\), where \(\lambda_0 = 500\space nm\), \(v = 75000\space m/s\), and \(c=3\times 10^{8}\space m/s\).

Step2: Substitute the values into the formula

\(\Delta\lambda=500\times\frac{75000}{3\times 10^{8}}\)
First, calculate \(\frac{75000}{3\times 10^{8}}=\frac{7.5\times 10^{4}}{3\times 10^{8}} = 2.5\times 10^{-4}\)
Then, \(\Delta\lambda=500\times2.5\times 10^{-4}\)
\(\Delta\lambda = 0.125\space nm\)

Answer:

\(0.125\)