Question

A radioactive substance (parent) decays to it's daughter element, the age of radioactive substance (t) is related to the daughter (d) parent (p) ratio by the equation :

• A. $t=\frac{1}{\lambda }ln(1+\frac{p}{d})$
• B. $t=\frac{1}{\lambda }ln(1+\frac{d}{p})$
• C. $t=\frac{1}{\lambda }ln\left(\frac{d}{p}\right)$
• D. $t=\frac{1}{\lambda }ln\left(\frac{p}{d}\right)$

Answer 1

Answer: (B)

$t=\frac{1}{\lambda }ln(1+\frac{d}{p})$

$N=N_0.e^{\lambda t};$ where N = Parent remaining (p)

and $N_0$ = Initial parent = Parent remaining (p) + daughter formed (d)

$p=(p+d).e^{-\lambda t}$ or $ln\frac{(p+d)}{p}=\lambda .t$

$t=\frac{1}{\lambda }ln\left(\frac{1}{+}\frac{d}{p}\right)$

Hence option (B) is correct.