A mixture consists of two radioactive materials $A_1$ and $A_2$ with half lives of $20 \mathrm{~s}$ and $10…

A mixture consists of two radioactive materials $A_1$ and $A_2$ with half lives of $20 \mathrm{~s}$ and $10 \mathrm{~s}$ respectively. Initially the mixture has $40 \mathrm{~g}$ of $A_1$ and $160 \mathrm{~g}$ of $A_2$. The amount of the two in the mixture will become equal after
  1. $60 \mathrm{~s}$
  2. $80 \mathrm{~s}$
  3. $20 \mathrm{~s}$
  4. $40 \mathrm{~s}$

Solution

For $40 \mathrm{~g}$ amount
$40 \mathrm{~g} \underset{\text { half -life }}{\stackrel{20 \mathrm{~s}}{\longrightarrow}} 20 \mathrm{~g} \stackrel{20 \mathrm{~s}}{\longrightarrow} 10 \mathrm{~g}$
For $160 \mathrm{~g}$ amount
$\begin{array}{l}
160 \mathrm{~g} \stackrel{10 \mathrm{~s}}{\longrightarrow} 80 \mathrm{~g} \stackrel{10 \mathrm{~s}}{\longrightarrow} 40 \mathrm{~g} \\
40 \mathrm{~g} \stackrel{10 \mathrm{~s}}{\longrightarrow} 20 \mathrm{~g} \stackrel{10 \mathrm{~s}}{\longrightarrow} 10 \mathrm{~g}
\end{array}$
So, after $40 \mathrm{~s} A_1$ and $A_2$ remains same.

Asked in: NEET 2012 (Screening)

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