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If the half lives of a radioactive element for $\alpha$ and $\beta$ decay are 4 years and 12 years respectively, the ratio of its inital activity and that after 12 years will be
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$6.25 \%$
$\begin{aligned} & \text { } T=\frac{T_\alpha T_\beta}{T_\alpha+T_\beta}=\frac{4 \times 12}{4+12}=3 \\ & n=\frac{t}{T}=\frac{12}{3}=4 \\ & \frac{N}{N_0}=\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^4=\frac{1}{16}=6.25 \%\end{aligned}$
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