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bmxicle
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Homework Statement
The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope 40K has a 1.28 billion year half-life and is naturally present as very low levels. 40K decays by beta emission into 40Ar. Argon is a gas, and there is no argon in flowing lava because the gas escapes. Once the lava solidifies, any argon produced in the decay is trapped inside and cannot escape. A geologist brings you a piece of solidified lava in which you find the 40Ar/40K ratio to be 0.12. What is the age of the rock
Homework Equations
N(t) = N(0)(1/2)t/t1/2
r = ln2/t1/2[/SUP]
The Attempt at a Solution
Here's what i have so far.
NAr is the number of argon atoms in the sample
NK is the number of pottasium atoms in the sample
K0 is the original number of pottassium atoms in the sample.
NAr/NK =0.12 ===> NAr = 0.12NK
Nk0 = NAr + Nk
These two equations combined give NK0 = 1.12Nk
and since Nk = NAr/0.12
===> NK0 = NAr1.12/0.12
Plugging this into the equation gives:
NAr = NAr1.12/0.12(0.5)t/t1/2
0.12/1.12 = (0.5)t/t1/2
T = T1/2(ln(0.12/1.12)/ln(0.5))
This gives me 4.1 billion years which isn't right.