Q139 / 155 · WBJEE 2017 · Physics
Radon- 222 has a half-life of 3.8 days. If one starts with $0.064 \mathrm{kg}$ of radon-222, the quantity of radon- 222 left after 19 days will be
- Correct answerA$0.002 \mathrm{kg}$
- B$0.062 \mathrm{kg}$
- C$0.032 \mathrm{kg}$
- D$0.024 \mathrm{kg}$
Solution
Half life of radon $=3 \cdot 8$ days
Total half-lives in 19 days
$\begin{array}{l}
=\frac{19}{3 \cdot 8} \\
=\frac{190}{38}
\end{array}$
$=5$ half-lives
Initially mass of radon $=0.064 \mathrm{kg}$
$0 \cdot 064 \frac{T_{1}}{T_{3}} 0 \cdot 032 \stackrel{T_{2}}{\longrightarrow}$
$0 \cdot 016 \stackrel{T_{4}}{\longrightarrow} 0 \cdot 004 \stackrel{T_{5}}{\longrightarrow} 0 \cdot 002$
So in five half-life periods, the Radon sample will reduce to $0.002 \mathrm{kg}$
$\text {Or } \frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{5}$
$\Rightarrow \quad N=0 \cdot 064 \times \frac{1}{32}$
$=0 \cdot 002 \mathrm{kg}$
Hence, the correct answer is option: 'A'.