Question

After $2$ hours $1 / 16$ 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

$N =N_{0}\left(\frac{1}{2}\right)^{n}$ $\frac{N_{0}}{16} =N_{0}\left(\frac{1}{2}\right)^{n}$ $\Rightarrow \left(\frac{1}{2}\right)^{4} =\left(\frac{1}{2}\right)^{n}$ $(\therefore n=4)$ Half-life $=\frac{\text { Total time }}{n}$ $=\frac{2}{4}$ $=0.5\, h$ $=30\, \min$