Question

A sample contains $10^{–2}$ kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is $\frac {x}{100}$. The value of $x$ is ______.

Answer 1

$N_1 = \frac {(\frac {10^{-2}}{1})}{24}$

$N_2 = \frac {(\frac {10^{-2})}{2}}{2^2}$

$⇒ \frac {N_1}{N_2}=\frac 12$

∴ Mass ratio of A and B ,

$\frac {m_1}{m_2}= \frac {N_1}{N_2} \times \frac {M_1}{M_2}$

$= \frac 12 \times (\frac 12)$

$= \frac 14$

$=\frac {25}{100}$
Given that, the ratio of the amounts of A and B after 16 s is $\frac {x}{100}$.
On comparing, $x = 25$

So, the answer is $25$.