Answer
$$4.3 \times 10^{8} $$
Work Step by Step
Since $R \propto 1 / T_{1 / 2}(\text { see } \mathrm{Eq} .42-20),$ the ratio of rates is
$$\frac{R_{\alpha}}{R_{\text {fision }}}=\frac{ {T_{1 / 2}}_{\text {fision }} } {{\mathrm{T}_{1 / 2}}_{\alpha} }=\frac{3.0 \times 10^{17} \mathrm{y}}{7.0 \times 10^{8} \mathrm{y}}=4.3 \times 10^{8} . $$
