# Modern Physics Help: K-40/Ar-40 Atom Ratio Analysis, Age Calculation

• rock.freak667
In summary, the analysis of a moon rock sample shows that the ratio of stable Ar-40 atoms to radioactive K-40 atoms is 10.3. Using the formula N=N_0e^{-\lambda t}, we can calculate the fraction of original K-40 atoms remaining in the rock, the number of half-lives that have elapsed, and the age of the rock. From these calculations, the age of the solar system can be deduced.
rock.freak667
Homework Helper

## Homework Statement

Analysis of potassium and argon atoms in a moon rock sample shows that the ratio of the number of stable Ar-40 atoms to the number of radioactive K-40 atoms is 10.3.
Assume that all the Ar atoms were produces by the decay of K atoms, with a half-life of 1.25x10^ years.
(i)Calculate:
a) the fraction of the original K-40 atoms remaining in the rock
b) the number of half-lives that has elapsed
c) the age of the rock.

(ii) From the answers above, deduce the age of the solar system.

## Homework Equations

$$N=N_0e^{-\lambda t}$$

## The Attempt at a Solution

Can someone guide me on how to start this?

"the number of stable Ar-40 atoms to the number of radioactive K-40 atoms is 10.3."

Now in the formula N=N_0exp(-$\lambda t$) N is the no. of radioactive atoms at time t, So I am a bit lost.

Last edited:
If N is the no. of radioactive atoms at time t and N_o is the no. of radioactive atoms at time t = 0, then what is N_o - N? And what is (N_o - N)/N ?

Well $N_0-N$ would be the number of radioactive atoms left at time t.

But how do I find N_0 or N since I don't have the value of N at t=0 or at any value for t?

(N_0 - N) is the number of stable atoms.
In the problem (N_0 - N)/N is given. And that is equal to [e^(lambda t)] -1.

## 1. What is the K-40/Ar-40 atom ratio analysis?

The K-40/Ar-40 atom ratio analysis is a method used in modern physics to determine the age of rocks and minerals. It is based on the radioactive decay of potassium-40 (K-40) to argon-40 (Ar-40) and is commonly used in geochronology.

## 2. How does the K-40/Ar-40 atom ratio analysis work?

The K-40/Ar-40 atom ratio analysis works by measuring the amount of K-40 and Ar-40 atoms present in a sample of rock or mineral. As K-40 decays, it produces Ar-40 atoms at a known rate. By comparing the amount of K-40 and Ar-40 present, scientists can calculate the age of the sample.

## 3. What is the importance of the K-40/Ar-40 atom ratio analysis in age determination?

The K-40/Ar-40 atom ratio analysis is important because it is a reliable and accurate method for determining the age of rocks and minerals. It is also useful for dating geological events and understanding the history of Earth's formation and evolution.

## 4. What are the limitations of the K-40/Ar-40 atom ratio analysis?

While the K-40/Ar-40 atom ratio analysis is a powerful tool in age determination, it does have some limitations. For example, it can only be used on rocks and minerals that contain potassium, and it is not suitable for materials that have been heated or altered since their formation.

## 5. How is the K-40/Ar-40 atom ratio analysis used in other fields of science?

The K-40/Ar-40 atom ratio analysis is not only used in geochronology, but it is also used in other fields such as archaeology, paleontology, and environmental science. It can be used to date fossils, artifacts, and sediments, providing valuable information about the history of Earth and its inhabitants.

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