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

Answer:

$v=-4.93\times 10^{5}~m/s$ [negative sign denotes that it is moving away]

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:

$\frac{\Delta \lambda}{\lambda} =-\frac{v}{c}$

$\frac{0.2}{121.6} =-\frac{v}{3\times 10^8}$

$v=-4.93\times 10^{5}~m/s$ [negative sign denotes that it is moving away]