Answer to Question #115613 in Quantum Mechanics for Vidurjah Perananthan

Question

The resting wavelengths (ie when the star is stationary) for the Balmers series lines are as follows:

In a spectral measurement of a star, the wavelength of 486,157 nm was measured.
a) What is the radial velocity of the star relative to the earth? By radial velocity is meant that the direction of velocity is an extension of the Earth's radius toward the star. In other words, "straight to or from" the Earth.
b) Was the movement directed at or away from us?

Answer 1

Laboratory wavelength is equal to $\lambda_0=486.133 \space{nm}$

The measured wavelength is $\lambda=486.157 \space{nm}$

From the formula for the Doppler effect

$\frac{\lambda-\lambda_0}{\lambda_0}=\frac{v}{c}$

 radial velocity is

$v= c\cdot\frac{\lambda-\lambda_0}{\lambda_0}=3\cdot10^5\cdot\frac{486.157-486.133}{486.133}=14.811 \space{km/s}$

The spectral line is shifted to the red side, therefore the star moves away from the Earth.