Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

•• The supernova explosion that is believed to have preceded the formation of our solar system created large quantities of radioactive nuclei. There are reasons to think that the isotopes 235U and 238U would have been created in roughly equal numbers. That is, the ratio N238/N235 was close to 1 at t = 0 (the time of the explosion), (a) Show that at any later time

where r235 and r238 denote the decay constants of 235U and 238U. (b) Use the data in Appendix D to find r235 and r238. (c) Use the observed abundances of 235U and 238U on earth today to estimate how long ago the supernova explosion occurred.