Q 12-13-085JEE MainJEE Main 2022 (24 Jun, Shift 2)Medium
A sample contains $10^{-2}\ \text{kg}$ each of two substances $A$ and $B$ with half lives $4\ \text{s}$ and $8\ \text{s}$ respectively. The ratio of their atomic weights is $1 : 2$. The ratio of the amounts of $A$ and $B$ after $16\ \text{s}$ is $\dfrac{x}{100}$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 25
In $16\ \text{s}$, $A$ goes through $4$ half-lives and $B$ through $2$ half-lives. Starting from equal masses, the remaining amounts (masses) are
$$m_A = \frac{10^{-2}}{2^4},\qquad m_B = \frac{10^{-2}}{2^2}$$
$$\frac{m_A}{m_B} = \frac{1}{4} = \frac{25}{100}\ \Rightarrow\ x = 25$$
Solution by Sreeraj P, M.Sc Physics