Question

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

$A=6.25\times {10}^{-4}kg,B=2.5\times {10}^{-3}kg$

The amount left after N half-lives

$N=N_0{\left[\begin{array}{c}\frac{1}{2}\end{array}\right]}^n$

For A, $n=\frac{t}{T_{\frac{1}{2}}}=\frac{16s}{4s}=4$

$N_A={10}^{-2}kg{\left[\begin{array}{c}\frac{1}{2}\end{array}\right]}^4=6.25\times {10}^{-4}kg$

For B, $n=\frac{16s}{8s}=2$

$N_B={10}^{-2}kg{\left[\begin{array}{c}\frac{1}{2}\end{array}\right]}^2=2.5\times {10}^{-3}kg$