Some Radiological Dating with Stoichiometry

In summary, the conversation discusses a problem involving the age of a rock sample based on its potassium-40 and argon-40 content. The problem involves assumptions about the origin of the argon-40 and how much potassium-40 would have to be present for the rock to be a certain age. The conversation also explores the concept of beta minus decay and the constant number of atoms of both elements.
  • #1
phost
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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

Homework Statement


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?)


Homework Equations


k = In 2/t1/2

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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  • #2
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?
 
  • #3
daveb said:
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.
 
  • #4
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.
 
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  • #5
Borek said:
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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FAQ: Some Radiological Dating with Stoichiometry

1. What is radiological dating?

Radiological dating is a method used by scientists to determine the age of a material or object by measuring the amount of radioactive elements it contains.

2. How does radiological dating work?

Radiological dating works by measuring the amount of radioactive isotopes present in a material and comparing it to the amount of stable isotopes. As radioactive isotopes decay over time, the ratio of radioactive to stable isotopes changes, allowing scientists to calculate the age of the material.

3. What is stoichiometry and how does it relate to radiological dating?

Stoichiometry is the study of the quantitative relationships between reactants and products in a chemical reaction. In radiological dating, stoichiometry is used to determine the initial amount of radioactive isotopes in a sample and the amount of stable isotopes produced through decay, which is essential for calculating the age of the material.

4. What are some common isotopes used in radiological dating?

Some common isotopes used in radiological dating include carbon-14, potassium-40, and uranium-238. These isotopes have long half-lives, making them useful for dating materials that are millions or even billions of years old.

5. How accurate is radiological dating?

Radiological dating can be accurate within a certain range, depending on the material being dated and the method used. It is most accurate for materials that are less than 50,000 years old, but can still provide reliable results for older materials. However, it is important to note that external factors, such as contamination, can affect the accuracy of radiological dating.

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