3. A fusion reaction important in solar energy production involves capture of a proton by a carbon nucleus, which has six times the charge of a proton and a radius of r = 2 X 10'15 m. (a) Estimate the Coulomb potential V experienced by the proton if it is at the nuclear surface. (b) The proton is incident upon the nucleus because of its thermal motion. Its total energy cannot realistically be assumed to be much higher than 10 kT, where k is Boltzmann's constant and where T is the internal temperature of the sun of about 107 0K. Estimate this total energy, and compare it with the height of the Coulomb barrier. (c) Calculate the probability that the proton can penetrate a rectangular barrier potential of height V extending from r to 2r, the point at which the Coulomb barrier potential drops to V/Z. (d) Is the penetration through the actual Coulomb barrier potential greater or less than through the rectangular barrier potential of part (c)