The ages of rocks that contain fossils can be determined using the isotope ^87Rb

Question

The ages of rocks that contain fossils can be determined using the isotope ^87Rb. This isotope of rubidium undergoes beta decay with a half-life of 4.75 times 10^10 y. Ancient samples contain a ratio of ^87Sr to ^87Rb of 0.0145. Given that 87Sr is a stable product of the beta decay of ^87Rb, and assuming there was originally no ^87Sr present in the rocks, calculate the age of the rock sample. Assume that the decay rate is constant over the relatively short lifetime of the rock compared to the half-life of ^87Rb.

Explanation / Answer

First calculate the constant k:
k = ln2/t1/2 = ln2/4.75x1010 = 1.46x10-11 y-1

Now we know that the ratio of Sr to Rb is: Sr/Rb = 0.0145
Sr = 0.0145Rb (1)

EDITED

We also know that Sr = Rbi - Rb ---> Rb + Sr = Rbi, (2)

Placing (1) in (2):
Rbi = 0.0145Rb + Rb = 1.0145Rb = Sr

If initially there were no Sr then to calculate the age:
C = Co exp(-kt)
1.0145[Rb] = [Rb]exp(-1.46x10-11t)
1.0145 = exp(1.46x10-11t)
ln(1.0145)/1.46x10-11 = -t
t = 3.01x109 y

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