Discussion Forum

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 

Answer:

Explanation:

Activity $\left(-\frac{dN}{dt}\right)=\lambda N=\left(\frac{1}{t_{mean}}\right)\times N$

$\therefore$  $N=\left(-\frac{dN}{dt}\right)\times t_{mean}$

 =Total number of atoms 

 Mass of one atom is  $10^{-25} kg=m(say)$

$\therefore$   Total mass of radioactive substance = (number of atoms) x (mass of onbe atom)

  $=\left(-\frac{dN}{dt}\right) (t_{mean})(m)$

 Substituting the values , we get

 Total mass of radioactive substance =1 mg

 $\therefore$  Answer is 1