Question

The ratio of the atoms of two elements $A$ and $B$ at radioactive equilibrium is $5.0\times {10}^5:1$ respectively. Calculate half life of $B$ if half life of $A$ is $245$ days.

Answer 1

Kf

$A\rightleftharpoons B$

Kb

$Keq=\frac{Kf}{Kb}=\frac{1}{5\times {10}^5}=\frac{\left[B\right]}{\left[A\right]}$

$\frac{{\left(t_{1/2}\right)}_B}{{\left(t_{1/2}\right)}_A}=\frac{\left(KA\right)}{\left(KB\right)}=\frac{\left[A\right]}{\left[B\right]}$

${\left(t_{1/2}\right)}_B=\frac{245\times 5\times {10}^5}{1}$

${\left(t_{1/2}\right)}_B=1225\times {10}^{5}days$