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

`(\lambda_0-\lambda_s)/(\lambda_s) = (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,

`(\lambda_0-\lambda_s)/(\lambda_s) = (v)/(c)`

`(\lambda_0-1375*10^(-9))/(1375*10^(-9)) = (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