Problem 5. (15 pts) In the "Big Bang", the universe started very hot, so hot that there were no nuclei, only separated nucleons. As the universe expanded, it cooled, and nucleons then started to clump together, forming the elements. However, the expansion was so fast that there was only time to form the light elements (hydrogen, deuterium, helium, and a little lithium) before the density was too small for clumping to occur. Elements heavier than these were formed much, much later, inside massive stars. The heavy elements got out of these stars after the stars had burned up all of their available nuclear fuel, and with nothing to keep them hot, they collapsed, rebounded, and blew most of their mass into interstellar space. In these collapsing and rebounding stars, the densities were at one point so large that any nuclei that could be made were made. In particular, let's assume that U238 and U235 were created in these stars with equal abundances. After this matter was ejected from the initial massive star (and went on to form the Earth), these uranium isotopes decayed, decreasing their abundances. The present-day relative abundance of U235 is 0.7%, much smaller than that of U238, 99.3%, because U235 has a shorter lifetime. The lifetimes of these isotopes are 1.02x10^9 years and 6.52x10^9 years, respectively. Using this information, estimate the time since these elements were ejected from the massive star.

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