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Some Radiological Dating with Stoichiometry

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phost
#1
Feb27-12, 09:20 AM
P: 6
It's kind of baffling me when I'm encountering this question in this sub-chapter. It's just unusual. So I really need your help :D

1. The problem statement, all variables and given/known data
If a rock sample was found to contain 1.16 10-7 mol of
argon-40, how much potassium-40 (t1/2 = 1.3 109 yr)
would also have to be present for the rock to be 1.3 109
years old? See assumption in Problem 14.84.

And the problem 14.84 question is ...

A 500 mg sample of rock was found to have 2.45 10-6
mol of potassium-40 (t1/2 = 1.3 109 yr) and 2.45
10-6 mol of argon-40. How old was the rock? (Hint: What
assumption is made about the origin of the argon-
40?)


2. Relevant equations
k = In 2/t1/2

3. The attempt at a solution
I just find out that the both K and Ar in periodic table have a closely enough molecular mass, which is 40 g/mol (39,1 for K and 39,95 for Ar). But it just weird when the molecular mass is multiplied with each moles of Ar and K to find mass, because it doesn't add up for 500 mg. Also I don't have any idea what does the t1/2 works for. Of course we could find the rate constant from the equation before for it.
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daveb
#2
Feb27-12, 09:42 AM
P: 925
What happens if you assume all the argon-40 originates from the potassium-40 beta minus decay? How much potassium had to be present in the rock for that much to decay?
phost
#3
Feb27-12, 10:14 AM
P: 6
Quote Quote by daveb View Post
What happens if you assume all the argon-40 originates from the potassium-40 beta minus decay? How much potassium had to be present in the rock for that much to decay?
Well, if I assume that, it is plausible because potassium-40 will lose 1 electron and becoming argon-40 with beta minus decay. But I still don't understand it, was the assumption says the rock originally a pure potassium-40 back then and becoming argon-40 in the whole time? Or is it in the first time the potassium-40 had 4.9x10-6 mole and in the meantime because of the beta minus decay it changed and split into two parts, the half of the potassium-40 with 2.45x10-6 mole and the other half with the same mole but the argon-40? My apologize if I don't get the idea.

Borek
#4
Feb27-12, 10:55 AM
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Some Radiological Dating with Stoichiometry

Potassium and argon are only a small part of the sample, so their masses don't have to add to 500 mg.

Or is it in the first time the potassium-40 had 4.9x10-6 mole and in the meantime because of the beta minus decay it changed and split into two parts, the half of the potassium-40 with 2.45x10-6 mole and the other half with the same mole but the argon-40?
That's what would happen exactly after half time. We assume rock was melted before and degassed, so all argon it contains now comes from the potassium-40 decay. And total number of atoms of both elements is constant.
phost
#5
Feb29-12, 04:01 AM
P: 6
Quote Quote by Borek View Post
Potassium and argon are only a small part of the sample, so their masses don't have to add to 500 mg.

Or is it in the first time the potassium-40 had 4.9x10-6 mole and in the meantime because of the beta minus decay it changed and split into two parts, the half of the potassium-40 with 2.45x10-6 mole and the other half with the same mole but the argon-40?
That's what would happen exactly after half time. We assume rock was melted before and degassed, so all argon it contains now comes from the potassium-40 decay. And total number of atoms of both elements is constant.
I hadn't considered that. That was really helpful, thanks a lot :D


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