The first step in nuclear fusion on the sun involves the collison of two protons, which form a deutron. Consider two protons far apart on a collison course with equal but opposite velocity. Their average kinetic energy is given by K = 1/2mv^2 = 3/2KbT where Kb is Boltzmann's constant and T is the Kelvin temperature. The reaction can only occur if the protons come into contact. The radius of a proton is rp = 10^-15 meters. What temperature is necessary for this to take place?
I believe that the most useful equations here are K.E. + P.E. = Total Energy
and Ea = Eb (energy at a is equal to energy at b)
The Attempt at a Solution
I have a strong feeling here that this problem is best solved using the laws of the conservation of energy. As a result I feel I can set the energy of the two protons equal to one another: KE1 + PE1 = KE2 + PE2.
The kinetic energy is given by 3/2KbT. So, I believe I can set
3/2KbT + PE1 = 3/2KbT + PE2. The problem then is that I need to have my potential. That's sort of where I'm stuck. My feeling is that if I had the potentials, I would be able to solve for T. But then again, will everything just cancel out? I sort of get the feeling that the radius of the proton is extra and unnecessary information. My research into this suggests the temperature I'm trying to derive is somewhere in the range of 10 to 15 million K.