Question

Rn decays into Po by emitting an $\alpha$ particle with half life of 4 days. A sample contains $6.4\times {10}^{10}$ atoms of Rn. After 12 days, the number of atoms of Rn left in the sample will be

• A. $3.2\times {10}^{10}$
• B. $0.53\times {10}^{10}$
• C. $2.1\times {10}^{10}$
• D. $0.8\times {10}^{10}$

Answer 1

The correct option is D $0.8\times {10}^{10}$

$\begin{array}{c}\text{Half Life}=t_{1/2}=4\text{days}\\ \text{Total time}=12\text{days}\\ T=n\times t_{1/2},n=\text{no. of half lives}\\ \begin{array}{c}12=n\times 4\\ \end{array}\\ n=3\end{array}$

$\begin{array}{cc}N& =N_0\times {\left(\frac{1}{2}\right)}^n.....\text{radioactivity equation}\\ N_0& =6+4\times {10}^{10}...\text{Given}\\ N& =6.4\times {10}^{10}{\left(\frac{1}{2}\right)}^3\\ & =\frac{6.4\times {10}^{10}}{8}\\ & =0.8\times {10}^{10}\end{array}$