Radioactive Age Dating, Part 2
Okay, so last time we were examining the decay of radioactive
isotopes, for example:
Here, 87Rb is referred to as the parent
isotope and 87Sr is referred to as the daughter
isotope.
And we found that the decay rate went like this:
But we don't know the initial abundances of the isotope.
So how can we age date?
We do know another piece of information: the
total amount of 87Rb + 87Sr stays constant!
So, time for some algebra. We had
Plugging and chugging,
we get
In practice, we examine isotopic ratios, comparing
to a stable isotope, for example (86)Sr.
Now, we just rearrange terms (and redo the notation a bit)
to get
We still have two unknowns
in this equation: t (time) and (87)Sr_0/(86)Sr
(the initial abundance ratio of the Sr isotopes). What now?
What does that last equation look like? A
line! So:
-
Measure the abundance
ratios at several places in the rock
-
Plot daughter isotope
vs parent isotope.
-
Fit a straight line to
the data. Then
So we can solve for t and the initial Sr isotopic abundance
ratios. Cool!
