# Homework Help: Finding the age of a rock

1. Jul 19, 2008

### Number1Ballar

1. The problem statement, all variables and given/known data
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?

2. Relevant 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.

3. 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?

2. Jul 19, 2008

### 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?

3. Jul 19, 2008

### 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..

4. Jul 19, 2008

### 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.