A sample of radioactive substance, whose half - life is 16 days, registers 32 decays per second. How long will it take for the rate of decay to reduce to 2 decays per second?
A. 80 days B. 64 days C. 48 days D. 32 days
Correct Answer: B
Explanation
Given data: Half-life \(T_{1 / 2}=16\) days Initial rate of disintegration \(A _{0}=\frac{32 \text { decays }}{\left(\begin{array}{c}\text { second rate of } \\ \text { disintegration } \\ \text { after time } t\end{array}\right)}\) \(A =\frac{2 \frac{\text { decays }}{\text { second }}}{\text { disintegration approach }}\) \(No _{ Tv }^{ T } \underset{ No }{2} \stackrel{ T _{ ig }}{\longrightarrow} \cdots\) or in terms of rate \(\Rightarrow 32 \stackrel{16 \text { days }}{\longrightarrow} 16 \stackrel{16 \text { days }}{\longrightarrow} 8 \stackrel{16 \text { days }}{\longrightarrow} 4 \stackrel{16 \text { days }}{\longrightarrow} 2\) Which gives a total time of \(16 \times 4=64\) days
