Question

From laboratory measurements, we know that a particular spectral line formed by hydrogen appears at a wavelength of 121.6 nanometers (nm). The spectrum of a particular star shows the same hydrogen line appearing at a wavelength of 121.8 nm. What is the receding speed of the star? c = 3x10^5 km/s

Answer 1

`v=-4.93* 10^(5)~m/s` [negative sign denotes that it is moving away]

Step-by-step explanation:

Actual wavelength of hydrogen spectral lines,
`\lambda=121.6~nm`

Apparent wavelength of hydrogen spectral lines from a star,
`\lambda'=121.8~nm`

So, shift in wavelength:

`\Delta \lambda=\lambda'-\lambda`

`\Delta \lambda=121.8-121.6`

`\Delta \lambda=0.2~nm`

Using Doppler's shift:

`(\Delta \lambda)/(\lambda) =-(v)/(c)`

`(0.2)/(121.6) =-(v)/(3* 10^8)`

`v=-4.93* 10^(5)~m/s` [negative sign denotes that it is moving away]