Temperature from Doppler Effect spectral broadening

[anotherghost]

Homework Statement

A doppler effect problem:

A sodium atom is emitting radiation at a wavelength of 6000 angstroms. When measured however the wavelength is widened to 6000 +/- 0.02 angstams. If this is primarily due to the doppler effect, what is the temperature of the sodium atom?

The Attempt at a Solution

For the doppler effect part, I solved 6000 + 0.02 = 6000 (1 + v/c) -> v = 1000, which also works for 6000 - 0.02 = 6000 (1 - v/c). However, now I do not know where to go to get the temperature of the atom. The back of the book says that it is around 700 degrees Kelvin.

Point me in the right direction?

 

[anotherghost]

Note: I have the idea of using the equipartition theorem, and the numbers come out right, but I'm worried about two things.

First, I think the prof said that we weren't supposed to need to know anything aside from what was written on the assignment, and the mass of sodium is not written on the assignment, which from what I understand is needed for the theorem to be applied here.

Second, the formula works when I use v = 1000, yielding around 700 K, but I don't think it should. If this thing is oscillating sinusoidally, 1000 should be the maximum velocity of the particle, not the velocity at any point in time. So, if we're taking the average velocity - which I believe we have to for the equipartition theorem - shouldn't we be using the root mean square velocity for the average velocity? Which would be 1000 / sqrt(2)?