# How Do Geologists Determine the Age of Rock Samples Using Isotopic Ratios?

• molly16
In summary, Geologists are able to calculate ages of rock samples through measurements of certain isotopic rations combined with known radioactive decay rates. Two such processes leading to stable isotopes are: 87Rb --> 87Sr 238Ur --> 206Pb Half life of 87Rb is 4.90x10^10 years while half life of 238Ur is 4.51x10^9 years.The isotopic ratios are: 87Sr/87Rb = 0.051 206Pb/238Ur = 0.71 Assuming the time the rock was formed it contained no 87Sr or 206Pb, calculate the age of
molly16

## Homework Statement

Geologists are able to calculate ages of rock samples through measurements of certain isotopic rations combined with known radioactive decay rates (all such decays being considered to adhere to 1st order kinetic rate laws). Two such processes leading to stable isotopes are:

87Rb --> 87Sr
238Ur --> 206Pb

Half life of 87Rb is 4.90x10^10 years while half life of 238Ur is 4.51x10^9 years.The isotopic ratios are:

87Sr/87Rb = 0.051
206Pb/238Ur = 0.71

Assuming the time the rock was formed it contained no 87Sr or 206Pb Calculate the age of the rock indicated by the isotopic ratios.

dA/dt = -k[A]

ln(A/Ao) = -kt

t1/2 = ln(2)/k

## The Attempt at a Solution

I tried solving for the rate constant using t1/2 = ln(2)/k
and rearranging it to k = ln(2)/t1/2 = 1.41 x 10^-11

Then to solve for the time for the decay of 87Rb I plugged the value into the equation ln(A/Ao) = -kt

ln (A/Ao) = ln (87Sr/87Rb) = ln (0.051) = -(1.41x10^-11)t

then I solved for t which is t = 2.1x10^11 years for the decay of the 87Rb
but the answer is supposed to be t = 3.517x10^9 years

Can someone please explain this question to me and tell me what I'm doing wrong?
Thanks!

Last edited:
I tried solving for the rate constant using t1/2 = ln(2)/k
... converting half-lives to mean lives, good.

Can someone please explain this question to me and tell me what I'm doing wrong?
If you have isotope X' and Y' and they decay to X and Y respecively, but at different rates, then, from the decay equations of X' and Y' you can get equations for how the amounts of X and Y change over time ... and thus how the ratio of X:Y changes with time.

You are given the ratio X:Y, and initial quantities of X and Y, and you have to find the time that has elapsed to turn the initial quantities into the final ratio.

I suspect you have been concentrating on the wrong isotope - on X':Y' instead of X:Y ... start by deriving the equation for the quantity of each decay product as a function of time.

Simon Bridge said:
... converting half-lives to mean lives, good.

I suspect you have been concentrating on the wrong isotope - on X':Y' instead of X:Y ... start by deriving the equation for the quantity of each decay product as a function of time.

so then
Ao = A (1-e^-kt)
Ao/A = 1-e^-kt
ln (Ao/A) = +kt

but I still get the same answer??

Simon Bridge said:

Ahh never mind I figured it out. Thanks.

Well done :)

For others googling here later:
I made a slight mistake earlier - you are given X:X' rather than X:Y.
I think your repeated mistake was that you were putting the ration as A/Ao or Ao/A... which was similar to my misreading.

## What is the Age of Rock Sample Chemistry Question?

The Age of Rock Sample Chemistry Question is a scientific inquiry that seeks to determine the age of a rock sample through chemical analysis. This can involve various methods such as radiometric dating or analyzing the chemical composition of the rock.

## Why is it important to determine the age of a rock sample?

Determining the age of a rock sample is important for a variety of reasons. It can provide valuable information about the geological history of an area, the evolution of the Earth, and the formation of different rock types. Additionally, knowing the age of a rock sample can help scientists understand past climate conditions and the potential for natural resources such as oil and minerals.

## How is the age of a rock sample determined through chemistry?

The age of a rock sample is determined through various chemical techniques. One common method is radiometric dating, which measures the ratio of radioactive elements to stable elements in a rock sample. Another approach is analyzing the chemical composition of the rock, such as the presence of certain isotopes or minerals that can indicate its age.

## What are the limitations of using chemistry to determine the age of a rock sample?

While chemistry can provide valuable information about the age of a rock sample, there are limitations to this method. For example, certain types of rocks may not contain enough radioactive elements for accurate radiometric dating. Additionally, external factors like weathering and contamination can affect the accuracy of chemical analysis.

## How can the age of a rock sample contribute to our understanding of the Earth?

Studying the age of rock samples can provide important insights into the Earth's history and evolution. It can help us understand past geological events and processes, such as plate tectonics and climate change. This knowledge can also be used to make predictions about the future of our planet and inform environmental and conservation efforts.

• Biology and Chemistry Homework Help
Replies
3
Views
3K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
5K
• Introductory Physics Homework Help
Replies
6
Views
6K
• High Energy, Nuclear, Particle Physics
Replies
1
Views
4K