JEE Advance - Physics (2011 - Paper 1 Offline - No. 22)
The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10$$-$$25 kg. The mass (in mg) of the radioactive sample is _________.
Answer
1
Explanation
Activity $$A = \lambda N$$, where $$\lambda$$ is decay constant and N is number of particles present. Therefore,
$$N = {A \over \lambda } = A\tau $$
where $$\tau$$ = 1 / $$\lambda$$ is the mean life of the sample. The mass of the sample is
$$M = mN = mA\tau $$
where m is mass of an atom. Therefore, the mass of the radioactive sample is
M = 10$$-$$25 $$\times$$ 1010 $$\times$$ 109 = 10$$-$$6 kg = 1 mg
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