Question

At time $t = 0$, activity of radioactive substance is $1600 \,Bq$, at $t = 8 \,s$ activity falls to $100 \,Bq$. The activity at $t = 2\, s$ is

• A. $400\,Bq$
• B. $800\,Bq$
• C. $200\,Bq$
• D. $600\,Bq$

Answer 1

Answer: (B)

$800\,Bq$

Answer 2

$R = R_{0}\left(\frac{1}{2}\right)^{n}$ where $n$ is the number of half-lives. Given : $R= \frac{R_{0}}{16}$ $\therefore\frac{R_{0}}{16} = R_{0}\left(\frac{1}{2}\right)^{2}$ or $n=4$ Four half-lives are equivalent to $8\, s$. Hence, $2 \,s$ is equal to one half-life. So, in one half-life activity will fall half of $1600$ Bq, i.e., $800$ B