Astrophysics Problem - Protons Collision Temperature at Washington U

[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, let's 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?

 

[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.

 

[Borxter]

Found this website that could help you out:

http://www.answers.com/topic/maxwell-boltzmann-distribution

The way I understand the problem is that you should write down the Coulumb potential for 2 protons, and then plug in the radius of a proton to calculate the energy required for 2 protons to come in contact. Then you can use this energy to figure out the velocity of the proton. When you have the velocity, you divide it by 10 to get the root mean squeare velocity. Then using the link above you can find the equation that relates the rms velocity to the temperature in M-B distribution. Then you just solve the equation.

Makes sense to me, but that's no guarantee it's rigth :/

 

[Tloh]

Found this website that could help you out:

http://www.answers.com/topic/maxwell-boltzmann-distribution

The way I understand the problem is that you should write down the Coulumb potential for 2 protons, and then plug in the radius of a proton to calculate the energy required for 2 protons to come in contact. Then you can use this energy to figure out the velocity of the proton. When you have the velocity, you divide it by 10 to get the root mean squeare velocity. Then using the link above you can find the equation that relates the rms velocity to the temperature in M-B distribution. Then you just solve the equation.

Makes sense to me, but that's no guarantee it's rigth :/

thanks :), makes sense