Astrophysics problem

1. Mar 24, 2005

Tloh

This is from Physics 312 Astrophysics at Washington University.

Question:

What temperature would be required for two protons to collide if quantum mechanical tunneling is neglected? Assume that nuclei having velocities ten times the root mean square (rms) value for the Maxwell-Boltzmann distribution can overcome the Coulomb barrier. Compare your answer with the estimated central temperature of the Sun.

My Rational:

I am stuck because I keep running in circles with this question. It asks to provide the temperature required for two protons to collide. Alright, good so far. Then it says that nuclei having velocities 10 times the rms will colide. Aren't these two statements in a loop? ie. the temperature controls the Maxwell-Boltzmann distribution and thus the rms and thus the 10rms and yet it is telling us that protons simply over the 10rms will collide. So, lets say the temperature is extremely low, the rms will be low and the 10rms will be low, but there will be a 10rms that exists... Any thoughts?

2. Mar 24, 2005

Data

The way that I read the question is this:

Find the temperature such that protons having ten times the rms velocity predicted by the Maxwell-Boltzmann distribution can overcome the Coulomb potential barrier and collide.

3. Mar 24, 2005