The formula for the relativistic Doppler shift is

where the sign of

depends on whether the observer and the source are approaching or receding. In this problem, there are two sources, and one of them is receding and one of them is approaching, so the difference in wavelength is

where now

is the speed (not the velocity) of a particle on the Sun's equator due to the Sun's rotation. Now,

and

so, we can rewrite equation (1) as

Now, we guess that the speed

is tiny compared to the speed of light. This is intuitive, because one normally does not think of relativistic speeds when one thinks of the Sun macroscopically. Thus, we set

Then equation (2) becomes

We are given

,

, so we can easily solve for

. We find that

This is indeed a nonrelativistic speed, so the approximation that

was a good one. Therefore, answer (B) is correct.