Question 375: Dual Nature of Matter and Radiation

Question

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 _________.

Accepted Answer

Activity $$A = \lambda N$$, where $$\lambda$$ is decay constant and N is number of particles present. Therefore,
$$N = {A \over \lambda } = A	au $$
where $$	au$$ = 1 / $$\lambda$$ is the mean life of the sample. The mass of the sample is
$$M = mN = mA	au $$
where m is mass of an atom. Therefore, the mass of the radioactive sample is
M = 10
$$-$$25
$$	imes$$ 10
10
$$	imes$$ 10
9
= 10
$$-$$6
kg = 1 mg

Dual Nature of Matter and Radiation

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 _________.

Integer / Numeric Answer Type