Question

an important line in the spectrum of stars occurs at a wavelength of 656 nm. imagine that you observe four stars from earth and discover that this absorption line is at the wavelengths shown in the table below for each of the stars. which of the stars is moving with the fastest speed?

c
b
none, they all move with the same speed
a
d

Explanation:

Step1: Calculate wavelength difference for each star

For star A: \(|\lambda-\lambda_0|=|600 - 656|= 56\) nm.
For star B: \(|\lambda-\lambda_0|=|700 - 656|=44\) nm.
For star C: \(|\lambda-\lambda_0|=|646 - 656| = 10\) nm.
For star D: \(|\lambda-\lambda_0|=|657 - 656|=1\) nm.

Step2: Relate wavelength difference to speed

According to the Doppler effect formula \(v = c\frac{\Delta\lambda}{\lambda_0}\) (where \(c\) is the speed of light, \(\Delta\lambda=|\lambda-\lambda_0|\), \(\lambda_0 = 656\) nm). Since \(c\) and \(\lambda_0\) are constants, the star with the largest \(|\lambda-\lambda_0|\) has the fastest speed.

Answer:

A. Star A