Question

In a laboratory, the Balmer-beta spectral line of hydrogen has a wavelength of 486.1 nm. If the line appears in a star's spectrum at 486.4 nm, what is the star's radial velocity (in km/s)? (Enter the magnitude.) km/s Is it approaching or receding? approaching receding Is this a blueshift or a redshift? blueshift redshift

Answer 1

185.15 km/s

It is receding, that's a redshift

Step-by-step explanation:

The radial velocity V of a star can be calculated by the formula:

V = c·Δλ/λ₀

Where c is the speed of light (3*10⁸m/s), Δλ is the wavelength shift (the difference between the wavelengths), and λ₀ is the wavelength that is not shifted (in this problem, 486.1 nm)

If we put the given data in the equation we're left with:

V =
`3*10^(8)m/s *((486.4-486.1))/(486.1)`

V = 185147.09 m/s

Converting the velocity to km/s:

`185147.09 (m)/(s) *(1km)/(1000m)` = 185.15 km/s

• Because the line of the star's spectrum appears at a wavelength greater than the wavelength measured in the laboratory, the star is receding, this is called a redshift.