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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

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Answer:

185.15 km/s

It is receding, that's a redshift

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 = [tex]3*10^{8}m/s *\frac{(486.4-486.1)}{486.1}[/tex]

V = 185147.09 m/s

Converting the velocity to km/s:

[tex]185147.09 \frac{m}{s} *\frac{1km}{1000m}[/tex] = 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.

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