Question

The age of a specimen '$t$' is related to the daughter/parent ratio by the equation:

• A. $t=\frac{1}{\lambda }\ln \left(\frac{D}{P}\right)$
• B. $t=\frac{1}{\lambda }\ln (1+\frac{P}{D})$
• C. $t=\frac{1}{\lambda }\ln (1+\frac{D}{P})$
• D. $t=\frac{1}{\lambda }\ln (2+\frac{D}{P})$

Answer 1

The correct option is C $t=\frac{1}{\lambda }\ln (1+\frac{D}{P})$

We know,

$\frac{D}{p}=e^{\lambda T}-1$

so, $e^{\lambda T}=1+\frac{D}{p}$

or, $\lambda T=ln(1+\frac{D}{p})$

or, $T=\frac{1}{\lambda }ln(1+\frac{D}{p})$