Question

A fresh radioactive mixture has short lived species $A$ and $B$. Both emit $\alpha$ − particles initially at 8000 particles per minute. 20 minutes later, they emit 3500 $\alpha$ − particles per minute. If the half – lives of the species $A$ and $B$ are 10 minutes and 500 hours respectively, then the ratio of activities of A : B in the initial mixture was:

• A. $4:6$
• B. $6:4$
• C. $3:4$
• D. $3:1$

Answer 1

The correct option is D $3:1$

$A\to X+{}_2^{4}He$
t=0 $A_o$
t=20 $\frac{A_o}{4}$

$B\to Y+{}_2^{4}He$
t=0 $B_o$
t=20 $B_o$
As, $t_{\frac{1}{2}}$ for $B$ is very high its amount can be assumed to remain remain same after 20 minutes.

$A_o+B_o$ = 8000
$\frac{A_o}{4}+B_o$ = 3500
$A_o$ = 6000
$B_o$ = 2000
$\frac{A_o}{B_o}$ = $\frac{3}{1}$