Question: Q. 2. (i) State the law of radioactive decay. Write the SI unit of ‘activity’.
(ii) There are $4 \sqrt{2} \times 10^{6}$ radioactive nuclei in a given radioactive sample. If the halflife of the sample is $20 \mathrm{~s}$, how many nuclei will decay in $10 \mathrm{~s}$ ?
$\mathrm{R}$ A [Foreign I 2017]
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Solution:
Ans. (i) Statement : Rate of decay of a given radioactive sample is directly proportional to the total number of undecayed nuclei present in the sample
[Alternatively : $-\frac{d N}{d t} \propto N$ ]
Unit $\rightarrow$ becquerel (Bq)
(ii)
$$ N=N_{0} e^{-\lambda t} $$
$$ \frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n} $$
$$ \begin{aligned} n & =\frac{t}{T_{1 / 2}}=\frac{10}{20}=\frac{1}{2} \ \Rightarrow \quad N & =4 \sqrt{2} \times 10^{6} \times\left(\frac{1}{2}\right)^{1 / 2} \ & =\sqrt{2} \times 10^{6} \text { nuclei } \end{aligned} $$
[CBSE Marking Scheme 2017]
Detailed Answer :
For solving numerical (part-ii), kindly refer to Q. 1 (ii) Short Answer Type Questions-II of Topic-I of this chapter.
