The H d line has a wavelength of 410.2 nm when observed in the laboratory. If the H d line appears in a stars spectrum at 410.0 nm, what is the radial velocity of the star?

Question

Quizplus · Accepted Answer

The H d line in the star's spectrum at 410.0 nm is redshifted from the laboratory wavelength of 410.2 nm. Using the formula for radial velocity, v = c*(observed wavelength - laboratory wavelength)/laboratory wavelength, where c is the speed of light, we get v = c*(410.0 nm - 410.2 nm)/410.2 nm = -146 km/s. The negative sign indicates that the star is moving toward the observer. Therefore, the best choice is B, 146 km/sec toward the observer. The difference in wavelengths between the laboratory value and the observed value is equal to the change in wavelength due to Doppler shift. Using the formula for Doppler shift, we can solve for the radial velocity:
Δλ/λ = v/c
where Δλ is the difference in wavelengths, λ is the laboratory wavelength, v is the radial velocity, and c is the speed of light.
Plugging in the given values, we get:
0.2 nm / 410.2 nm = v/c
Solving for v, we get:
v = 0.2 nm / 410.2 nm * c = 61.6 km/sec
Since the observed wavelength is shorter than the laboratory wavelength (blue-shifted), the star must be moving toward the observer. Therefore, the answer is B.

The H D Line Has a Wavelength of 410