Question

The radioactivity of a certain material drops to $\frac{1}{16}$ of the initial value in $2$ hours. The half life of this radionuclide is

• A. 10 min
• B. 20 min
• C. 30 min
• D. 40 min

Answer 1

Answer: (C)

30 min

Answer 2

After $n$ half-lives the quantity of a radioactive substance left intact (undecayed) is given by $N =N_{0}\left(\frac{1}{2}\right)^{n}$ $=N_{0}\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$ Here, $N =\frac{1}{16} N_{0}, t=2 h$ $\frac{1}{16} N_{0} =N_{0}\left(\frac{1}{2}\right)^{2 / T_{1 / 2}}$ $\left(\frac{1}{2}\right)^{4} =\left(\frac{1}{2}\right)^{2 / T_{1 / 2}}$ Equating the powers on both sides $4 =\frac{2}{T_{1 / 2}}$ $T_{1 / 2} =\frac{1}{2} h=30 \,min$