Question

After 2 h $\frac{1}{16} th$ of initial amount of a certain radioactive isotope remains undecayed. The half-life of the isotope is

• A. 15 min
• B. 30 min
• C. 45 min
• D. 60 min

Answer 1

Answer: (B)

30 min

Answer 2

If N be the number of radioactive substance, left at some instant of time and $N_0$ be the number of atoms initially present in the substance, then number of atoms left after n-half lives is given by N = $N_0 \big(\frac{1}{2}\big)^n .$ Given, $\frac{N}{N_0} = \frac{1}{16}$ $\therefore \frac{1}{16} = \big(\frac{1}{2}\big)^n$ $\frac{1}{16} = \frac{1}{2^4}$ $\Rightarrow n = 4$ Also $n = \frac{t}{T^{1/2}}$ $T_{1/2} = \frac{t}{n} = \frac{2}{4} \times 60 \, min = 30 \, min$