Question

A radioactive substance (parent) decays to its 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

The correct option is B $t=\frac{1}{\lambda }\ln (1+\frac{d}{p})$

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