Question

The activity of a radioactive element reduces to $\frac{1}{16}$ of its original value in 36 years. The half life of the element is

• A. 6 years
• B. 9 years
• C. 12 years
• D. 18 years

Answer 1

The correct option is B

9 years

Activity at a given time is proportional to the number of radioactive atoms present at that time. The number of atoms left undecayed after 36 year $=\frac{1}{16}$ of the initial value, i.e. $N=\frac{N_0}{16}$
From $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$, we get n = 4. Now $t=n{T}_{\frac{1}{2}}$
Hence
$T_{\frac{1}{2}}=\frac{t}{n}=\frac{36years}{4}=9years.$
Hence the correct choice is (b)