A distant star emits light of wavelength 620 nm. As measured by an Earth observer, the light is shifted to 635 nm. Assuming the star is moving either away (positive radial velocity) or toward (negative radial velocity) Earth, what is its radial velocity relative to Earth?

Question

Quizplus · Accepted Answer

First, we use the formula for redshift to find the ratio of the observed wavelength to the emitted wavelength:
z = (observed wavelength - emitted wavelength)/emitted wavelength
z = (635 nm - 620 nm)/620 nm
z = 0.024
Next, we use the formula for Doppler shift to relate this redshift to the radial velocity:
z = (Δλ/λ) = v/c
where Δλ is the difference between the observed and emitted wavelengths, λ is the emitted wavelength, v is the radial velocity, and c is the speed of light.
0.024 = v/c
v = 0.024c or -0.024c
The negative sign indicates that the star is moving away from Earth, so the correct answer is B.

A Distant Star Emits Light of Wavelength 620 Nm