When a star like the Sun expands to become a red giant, its surface will move outward at about 10 km/s. For an observer looking directly at the Sun, what will be the Doppler-shifted wavelength of the H _$\alpha$ line (in nm)? From a source at rest, the H _$\alpha$ wavelength is 656.28 nm.

Question

Quizplus · Accepted Answer

The Doppler shift formula is:$$\lambda_{obs}=\lambda_0(1+\frac{v}{c})$$where:$$\lambda_{obs}$$ is the observed wavelength$$\lambda_0$$ is the rest wavelengthv is the velocity of the sourcec is the speed of lightIn this case, the velocity of the source is 10 km/s and the rest wavelength is 656.28 nm. Plugging these values into the formula, we get:$$\lambda_{obs}=656.28 nm(1+\frac{10 km/s}{3	imes10^8 m/s})$$$$\lambda_{obs}=656.28 nm(1.000033)$$$$\lambda_{obs}=656.30 nm$$Therefore, the correct answer is C) 656.30.

When a Star Like the Sun Expands to Become a Red