$4)$ Spent nuclear fuel is radioactive. a$)$ Suppose you have a kilogram of spent nuclear fuel. $99\%$ of the nuclear fuel $(990$ g$)$ is Uranium $238,$ while the remaining $1\%(10$ g$)$ is Strontium $90.$ How many Uranium atoms are in your sample? How many Strontium atoms are in your sample? Assume the uranium $238$ has a mass of $238$ grams per mole and strontium has a mass of $90$ grams per mole. Avogadro$$s number is $6\mathrm{.}0$e$+23.$ b$)$ Strontium has a half life of $30$ years while the Uranium has a half life of $4$ billion years. How many years must pass before the decay rate of Strontium $($decays per second$)$ is equal to the decay rate of the Uranium. $($Hint: Use the fact that the decay rate for any radioactive substance is equal to N$,$ where N $=$ N$0$e $$t$,$ set the two rates equal to each other, and solve for t$.)$

answer:

a$)$ Nu $=2\mathrm{.}5$e$24$ atoms, Ns $=6\mathrm{.}67$e$22$ atoms

b$)650$ years$($strontium is way more radioactive, and so decays faster$)$