Question

A radioactive nuclide decays at such a rate that after $96$ min, only $1/8th$ of the original amount remains. The value of half-life of the nuclide is

• A. 32 min
• B. 12 min
• C. 48 min
• D. 24 min

Answer 1

Answer: (A)

32 min

Answer 2

$N=\left(\frac{1}{2}\right)^{n} N_{0}$ $N_{0}=$ Initial amount, $N =$ Amount at ' $t$' time $n =$ no. of half lives. Given, $\frac{N}{N_{0}}=\frac{1}{8}$ $\Rightarrow\left(\frac{1}{2}\right)^{n}=\frac{1}{8} =\left(\frac{1}{2}\right)^{3}$ $\Rightarrow n=3$ As by definition, $n=\frac{\text { Total time }}{\text { Half-life time }}$ $\Rightarrow$ Half-life time $=\frac{96}{3}=32$ minutes.