Answer
a) -0.284 nm
b) Blue shift
c) $5.764\times10^{9}$ years
Work Step by Step
a) The speed of Andromeda Galaxy is small compared to the speed of light, so we use the formula $\Deltaλ=λ_{rest}(\frac{v}{c})$. Velocity of the galaxy is negative since it is approaching us. $$\Deltaλ=656nm(\frac{-130000m/s}{3\times 10^{8}m/s})=-0.284 nm$$
b) Since the galaxy is approaching and the wavelength has decreased, this is a blue shift.
c) Assuming that their velocity remains the same, time can be calculated using the formula $t=(\frac{d}{v})$. $$t=\frac{2.5\times 10^{6} ly}{130000m/s}(\frac{9.46\times 10^{15}}{1 ly})(\frac{1 year}{3.156\times 10^{7}s})=5.764\times 10^{9} years$$
