Spectral lines are fuzzy due to two effects: Doppler broadening and the uncertainty princi...

Spectral lines are fuzzy due to two effects: Doppler broadening and the uncertainty principle. The relative variation in wavelength due to the first effect (see Exercise 2,57) is given by

where T is the temperature of the sample and m the mass of the particles emitting the light. The variation due to the second effect (see Exercise 4.72) is given by

where Δt is the typical transition time.

(a) Suppose the hydrogen in a star has a temperature of 5 X 104 K. Compare the broadening of these two effects for the first line in the Balmer series (i.e.ni=3→nf=2). Assume a transition time of 10-8 s. Which effect is more important?

(b) Under what condition(s) might the other effect predominate?