How Old Is the Rock Using Potassium-Argon Dating?

[Number1Ballar]

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 at 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 of ⁴⁰K 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=N₀(1/2)^t/t[1/2]

where N is the number of nuclei, N₀ is the initial number of nuclei, t is time allowed to decay and t[1/2] is the half life.

The Attempt at a Solution

I actually do not know where to start with this one. I'm not sure how to apply the ratio given, and what variable I am even looking for, or if I'm even supposed to look at the relevant equation.

Could someone please point me in the right direction?

Thanks in advanced!

 

[lonewolf5999]

Your equation can be rewritten as

N/N₀=(1/2)^t/t[1/2]

Can you see a link between the ratio N/N₀ and the Ar/K ratio given in the question?

 

[Number1Ballar]

yes I think I see the connection..

0.12 = (1/2)^{t/1.28billion}??

solving for t? I don't get the right answer though

ln(.12) = t/1.25billion(ln.5) is what I was trying..

 

[lonewolf5999]

You'll need to be careful about the value you use for the N/N₀ ratio. N is the number of undecayed parent nuclei, not the daughter nuclei formed from the radioactive decay.