Question

If the peak wavelength of a star at rest is 1375 nm, then what peak wavelength is observed when the star is traveling 975,000 m/s away from the Earth.

Answer 1

The concept required to solve this problem is that of the Doppler effect which is defined as the change in frequency of a wave in relation to an observer who is moving relative to the wave source

Mathematically it can be expressed as

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

Where,

c = Speed of light

$\lambda_0$ = Peak wavelength

$\lambda_s$ = Peak Wavelength observed

Our values are given as,

$v=975000m/s$

$c = 3*10^8m/s \rightarrow$ Speed of light

$\lambda_s = 1375*10^{-9}m$

Basically what we should look for is that 'relative' frequency that is emitted when the star moves away so we clear $\lambda_s$

Replacing we have,

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

$\frac{\lambda_0-1375*10^{-9}}{1375*10^{-9}} = \frac{975000}{3*10^8}$

$\lambda_0 = 1379.46nm$

Therefore the peak wavelength that is observed when the star is traveling away from the eart to the velocity given is 1379.46nm