Calculating Wavelength of H_α for a Receding Star

[azatkgz]

Homework Statement

One of the most prominent spectral lines of hydrogen is $$H_\alpha$$ line.A bright red light with wavelength of $$656.1\times 10^{-9}m$$.What's the expected wavelength of the $$H_\alpha$$ line from a star receding with a speed of 3000 km/s?

The Attempt at a Solution

Is it just $$\lambda=\lambda_o-\frac{\lambda_ov}{c}$$

 

[BerryBoy]

Homework Statement

One of the most prominent spectral lines of hydrogen is $$H_\alpha$$ line.A bright red light with wavelength of $$656.1\times 10^{-9}m$$.What's the expected wavelength of the $$H_\alpha$$ line from a star receding with a speed of 3000 km/s?

The Attempt at a Solution

Is it just $$\lambda=\lambda_o-\frac{\lambda_ov}{c}$$

I believe that should be: $$\lambda=\lambda_o+\frac{\lambda_ov}{c}$$

When objects move away from the observer, the doppler shift, increases the wavelength (red-shifts it).

Sam

 

[ogb p]

where \lambda_o is the observed wavelength, v is the speed of recession, and c is the speed of light?

Yes, that is the correct formula to use. In this case, we can plug in the values given for the observed wavelength (656.1 nm) and the recession speed (3000 km/s) to solve for the expected wavelength of the H_alpha line. This would result in a wavelength of approximately 657.0 nm, slightly longer than the observed wavelength due to the receding motion of the star. This is known as the Doppler effect, where the wavelength of light is shifted due to the relative motion between the source and observer. This can be a useful tool for studying the motion and velocity of stars in our universe.