The reason that stars shine is that nuclear fusion is occurring under the intense pressures and temperatures reached in their cores. This fusion releases energy, which provides an outward pressure counteracting gravity, which prevents the star from collapsing. But, this process only works so long as fusion actually produces extra energy: if it did not, then there would be no explosive force to counteract gravity, and the star would collapse (this does indeed happen, and is the cause of supernovae and black hole formation at the end of a star's life). How much energy is produced via fusion is given by the binding energy of the atomic nucleus: when the binding energy is increasing, fusion reieases energy, but ifthe binding energy is decreasing then it actually consumes energy. BE A A 62Ni 24Mg 9 20Ne Fe Zn Kr Mo Ca Te Sm Lu 160 Hg -7.6 8 Ra 2380 12CU ^Hel 7 11B 6 GLi Binding energy per nucleon (MeV per nucleon) 5 Fusion produces 4 energy 3 3He 2 80 20 40 60 Number of Protons in the NucleusA simplified model of this process shows the binding energy is approximately given as a function of the number of protons p below bun) = 5% 1'12?) 10 Looking at the graph, this appears to switch from increasing to decreasing somewhere around p = 30, but it's hard to tell exactly where. as it is a rather gradual shift. Can you use Newton's method to help you find the exact place where fusion stops producing energy for the star? Do enough iterations of Newton's method to be sure the whole number portion of your answer is correct (remember, p is a number of protons, so we only care about its whole number value. and not about the decimal part). What is the critical value ofp? What element is this, beyond which stars can no longer function