Question

A sample contains $10^{-2}kg$ each of the two substances $A$ and $B$ with half-lives $4s$ and $8s$ respectively. Their atomic weights are in the ratio of $1:2$, the amounts of $A$ and $B$ after an interval of $16s$ are

• A. $A=0.625\times 10^{-4}kg,B=0.25\times 10^{-3}kg$
• B. $A=0.25\times 10^{-3}kg,B=0.625\times 10^{-4}kg$
• C. $A=2.5\times 10^{-3}kg,B=6.25\times 10^{-4}kg$
• D. $A=6.25\times 10^{-4}kg,B=2.5\times 10^{-3}kg$

Answer 1

Answer: (D)

The amount left after $N$ half-lives
$N=N_0{\left[\frac{1}{2}\right]}^n$
For A , $n=\frac{t}{T_{\frac{1}{2}}}=\frac{16s}{4s}=4$
$N_A=10^{-2}kg{\left[\frac{1}{2}\right]}^4=6.25\times 10^{-4}kg$
For B, $n=\frac{16s}{8s}=2$
$N_B=10^{-2}kg{\left[\frac{1}{2}\right]}^2$
$=2.5\times 10^{-3}kg$