Question

The activity of a freshly prepared radioactive sample is ${10}^{10}$ dps whose mean life is ${10}^9$ second. The mass of an atom of this radioisotope is ${10}^{25}$ kg. The mass in mg of a radioactive sample is ..........

• A. $1mg$
• B. $2mg$
• C. $3mg$
• D. none of these

Answer 1

The correct option is A $1mg$

Rate of decay = $\frac{1}{\tau }\times$ No of atoms undergoing decay

Therefore,
${10}^{10}=\frac{1}{{10}^9}\times No.$ of atoms undergoing decay

Number of atoms undergoing decay = ${10}^{19}$
Mass of ${10}^{19}$ atoms = ${10}^{19}\times {10}^{25}kg$

$={10}^{-6}kg=1mg.$