Nuclear Fusion in the Sun The source of the sun's energy is a sequence of nuclear reactions that occur in its core. The first of these reactions involves the collision of two protons, which fuse together to form a heavier nucleus and release energy. For this process, called nuclear fusion, to occur, the two protons must first approach until their surfaces are essentially in contact.
(a) Assume both protons are moving with the same speed and they collide head-on. If the radius of the proton is 1.2 X 10-15 m, what is the minimum speed that will allow fusion to occur? The charge distribution within a proton is spherically symmetric, so the electric field and potential outside a proton are the same as if it were a point charge. The mass of the proton is 1.67 X 10-27 kg.
(b) Another nuclear fusion reaction that occurs in the sun's core involves a collision between two helium nuclei, each of which has 2.99 times the mass of the proton, charge + 2e, and radius 1.7 X 10-15 m. Assuming the same collision geometry as in part (a), what minimum speed is required for this fusion reaction to take place if the nuclei must approach a center-to-center distance of about 3.5 X 10-15 m? As for the proton, the charge of the helium nucleus is uniformly distributed through out its volume.
(d) The temperature in the sun's core is about 1.5 X 107 K. How does this compare to the temperatures calculated in part (c)? How can the reactions described in parts (a) and (b) occur at all in the interior of the sun?