If the half-lives of a radioactive element for $α$ and $β$ decay are 4 year and 12 years respectively, then the percentage of the element that remains after 12 year will be -
Answer & explanation
Correct answer: option 1
Effective half life of decay is $T = \frac{4\times 12}{4+12} = 3 years$
$ n = \frac{t}{T} = \frac{12}{3} = 4$
$\frac{N}{N_0}=(\frac{1}{2})^{n}=(\frac{1}{2})^4=\frac{1}{16}$
Percentage remains after 12 years is $\frac{100}{16}\%=6.25\%$