The Sun is powered by nuclear fusion. In each chain reaction, four hydrogen nuclei fuse together to become a single helium nucleus. The total combined mass of the individual hydrogen nuclei before the reaction is greater than the mass of the helium nucleus. The mass lost as a result of this chain reaction is turned into energy according to Einstein's famous equation, E = mc". Consider the first part of the chain reaction in which two hydrogen nuclei (each a single proton) fuse. Figure A below shows the potential energy curve of a two-proton system. Energy in this graph is given in kev, where "ev" is the abbreviation for the unit electron-volt and 1 ev = 1.6 x 10 19 J. When the protons are more than about 2 fm (2 x 10*25 m) apart, the potential energy is positive. When the protons are close together, the potential energy is negative, and the protons are fused. Figure B below shows a close up of the potential energy curve when the protons are far apart. U (ke V) 800 700 600 U (keV) soo HOO 300 200 100 -100 10 15 20 25 30 - r (fm) 500 600 700 * r (fm) (a) What is the minimum mechanical energy required for the two protons to fuse? Give your answer in kev. kev fm (b) The mechanical energy of an average two-proton system in the Sun is around 2 kev. What is the minimum distance between the protons in such a system? (c) Explain why it seems impossible for fusion to take place in the Sun. Note: Of course, fusion must take place in the Sun. Although it seems impossible according to classical mechanics, quantum mechanics (Part VI) makes fusion possible. According to quantum mechanics, the seemingly mpossible is merely improbable, and even events with a low probability of occurrence may still happen. Because there are so many protons in the Sun, there is a good chance that at any moment many of them will fuse.A stellar black hole may form when a massive star dies. The star collapses down to a single point. Our Sun will not become a black hole because it does not have enough mass, so let us imagine a black hole with seven times the mass of the Sun. A single point has no radius, but a black hole has an effective radius known as the Schwarzschild radius. If an object gets inside the Schwarzschild radius, it never escapes. The Schwarzschild radius of a seven-solar-mass black hole is about 20.7 km. a) Find the escape speed using the Schwarzschild radius. Im/s (b) Compare your answer to the speed of light and speculate on how these objects got the name "black hole."