JEO495-radiometric-dating
Decay of Rubidium to Strontium
$$\ce{^{87}_{37}Rb -> ^{87}_{38}Sr + e^- + \bar{\nu}_e}$$
$$\ce{^{87}_{38}Sr (t) = ^{87}_{38}Sr (0) + ^{87}_{37}Rb (\mathrm{e}^{\lambda t} - 1)}$$
$\ce{\lambda}$ stands for the decay constant for Rubidium (Steiger and Jager, 1977)
$$\ce{\lambda = 1.42 * 10^{-11}} years^{-1}$$
The amount of $\ce{^{86}_{38}Sr}$ is constant since it's a stable isotope, therefore:
$$\cfrac{^{87}_{38}Sr}{^{86}_{38}Sr} \ce{=} \left(\cfrac{^{87}_{38}Sr}{^{86}_{38}Sr}\right)_0 \ce{+} \cfrac{^{87}_{37}Rb}{^{86}_{38}Sr} \ce{(\mathrm{e}^{\lambda t} - 1)}$$
Thus, t (age) can be defined as,
$$t = \cfrac{1}{\lambda} \ln{(\cfrac{\cfrac{^{87}_{38}Sr}{^{86}_{38}Sr} \ce{-} \left(\cfrac{^{87}_{38}Sr}{^{86}_{38}Sr}\right)_0}{^{87}_{37}Rb \ce{/} ^{86}_{38}Sr} \ce{+} 1)}$$
Here, $\ce{\cfrac{\cfrac{^{87}_{38}Sr}{^{86}_{38}Sr} \ce{-} \left(\cfrac{^{87}_{38}Sr}{^{86}_{38}Sr}\right)_0}{^{87}_{37}Rb \ce{/} ^{86}_{38}Sr}}$ can be treated as the slope denoted with m, thus:
$$t = \cfrac{1}{\lambda} \ln{(m \ce{+} 1)}$$
I will also add the U-Th-Pb series here later on.
Course Instructor: Dr. Biltan Kurkcuoglu
