The isotope ${}^{235}U$ decays by alpha emission with a half-life of $7.0\times 10^{8}y$. It also decays (rarely) by spontaneous fission, and if the alpha decay did not occur, its half-life due to spontaneous fission alone would be $3.0\times 10^{17}y$.
(a) At what rate do spontaneous fission decays occur in $1.0g$ of ${}^{235}U$?
(b) How many ${}^{235}U$ alpha-decay events are there for every spontaneous fission event?