Question

A radioactive sample is emitting $64$ times radiations than non-hazardous limit. If its half life is $2h$, after what time it becomes non-hazardous?

• A. 16 h
• B. 12 h
• C. 8 h
• D. 4 h

Answer 1

Answer: (B)

12 h

Answer 2

First calculate the amount left after $n$ half-lives and then time taken. $\frac{N_{t}}{N_{0}}=\left(\frac{1}{2}\right)^{n}$ where, $N_{t}=1$ amount left after expiry $n$ half lives $=1$ $N_{0}=$ initial amount $=64$ $\therefore \frac{1}{64}=\left(\frac{1}{2}\right)^{n}$ or $\left(\frac{1}{2}\right)^{6}=\left(\frac{1}{2}\right)^{n}$ $\therefore n=6$ Given, $t_{1 / 2}=2 h$ $\therefore$ Time taken $(T)=t_{1 / 2} \times n=2 \times 6$ $=12\, h$