Q69 / 69 · JEE Advanced 2011 (Paper 1) · Physics
The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^{-9} \mathrm{~s}$. The mass of an atom of this radioisotope is $10^{-25} \mathrm{~kg}$. The mass (in $\mathrm{mg}$ ) of the radioactive sample is
Correct answer: 1
Solution
Activity $\left(-\frac{d N}{d t}\right)=\lambda N=\left(\frac{1}{t_{\text {mean }}}\right) \times N$
$$
\begin{aligned}
& \therefore \quad N=\left(-\frac{d N}{d t}\right) \times t_{\text {mean }} \\
& \quad=\text { Total number of atoms } \\
& \text { Mass of one atom is } 10^{-25} \mathrm{~kg}=m \text { (say) } \\
& \therefore \quad \text { Total mass of radioactive substance } \\
& =(\text { number of atoms) } \\
& \quad \times(\text { mass of one atom) } \\
& =\left(-\frac{d N}{d t}\right)\left(t_{\text {mean }}\right)(m)
\end{aligned}
$$
Substituting the values, we get
Total mass of radioactive substance
$$
=1 \mathrm{mg}
$$
$\therefore$ Answer is 1 .
Analysis of Question
Question is very simple. Again in my opinion one can solve it.
Hence, the correct answer is 1.