Modern Physics 3 Question 29
30. The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^{-9} s$. The mass of an atom of this radioisotope is $10^{-25} kg$. The mass (in $mg$ ) of the radioactive sample is
(2011)
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Solution:
- Activity $-\frac{d N}{d t}=\lambda N=\frac{1}{t _{\text {mean }}} \times N$
$\therefore \quad N=-\frac{d N}{d t} \times t _{\text {mean }}=$ Total number of atoms
Mass of one atom is $10^{-25} kg=m$ (say)
$\therefore$ Total mass of radioactive substance
$$ \begin{aligned} & =(\text { number of atoms }) \times(\text { mass of one atom }) \\ & =-\frac{d N}{d t}\left(t _{\text {mean }}\right)(m) \end{aligned} $$
Substituting the values, we get
Total mass of radioactive substance $=1 mg$
$\therefore$ Answer is 1 .
