In hydrogen, the transition from level 2 to level 1 has a rest wavelength of 121.6 nm. Suppose you see this line at a wavelength of 120.5 nm in Star A, at 121.2 nm in Star B, at 121.9 nm in Star C, and at 122.9 nm in Star D. a. Which of these stars are coming toward us? And which ones are moving away?

b. Which star is moving fastest relative to us?

Given dа ta:

rest wavelength = λ₀=121.6nm

Star A wavelength = λa=120.5nm

Star B wavelength = λb=121.2nm

Star C wavelength = λc=121.9nm

Star D wavelength = λd=122.9nm

According to Doppler shift formula,

we have

v/c = (λ-λ₀) / λ₀

As we know c=speed of light=3*10^8m/s⁻¹

a.

Star A: v = (120.5-121.6) (3*10^8) / 121.6 = - 2.71*10^6m/s (towards)

Star B: v = (121.2-121.6) (3*10^8) / 121.6 = - 9.87*10^5m/s (towards)

Star C: v = (121.9-121.6) (3*10^8) / 121.6 = 7.40*10^5m/s (away)

Star D: v = (122.9-121.6) (3*10^8) / 121.6 = 3.21*10^6m/s (away)

b.

Star D is moving fastest relative to us.