Final answer:
The velocity of Rigel relative to Earth can be calculated using the Doppler effect formula. Plugging in the given values, we find the velocity to be approximately 2.94x10^3 m/s.
Step-by-step explanation:
The Doppler effect is a phenomenon that causes a shift in the observed wavelength of light when the source of the light is moving relative to the observer. This effect can be used to determine the velocity of a star relative to Earth.
In this case, the shift in the wavelength of the hydrogen line in Rigel's spectrum is given as 4.26x10^10 Hz. We can use the formula for the Doppler effect to calculate the velocity of Rigel relative to us:
v = (Δf/f_0) * c
where v is the velocity, Δf is the shift in frequency, f_0 is the initial frequency, and c is the speed of light.
Plugging in the values:
v = (4.26x10^10 Hz / 6.17x10^14 Hz) * 3x10^8 m/s
Solving this equation gives us a velocity of approximately 2.94x10^3 m/s.