Post a New Question

chemistry ugg!

posted by .

what is the age of a rock whose

Argon 40 / Potassium 40 ratio is 1.55?

The half life of Potassium 40 is 1.28 x 10^9 years

I am confused on this question theres no examples in my book but i have to know it can someone explain to me how to get to the answer?



You don't say if this is mass ratio or not. I will assume it is an atom ratio.
Start with any number you wish. Let's start with 100 atoms.
Let X = # atoms Ar at some time.
then 100 - x = # atoms K at that time.
Then Ar atoms/K atoms = (X)/(100-X) =1.55.
Solve for X to give # atoms of Ar and 100-X to give # atoms of K.

Then ln(No/N) = kt

k = 0.693/(t1/2) = 0.693/1.28 x 10^9 yrs.
No will be 100
N will be X
Solve for t.
Check my thinking. Check my work.


ok i get up to this part

k = 0.693/(t1/2) = 0.693/1.28 x 10^9 yrs.
which is the decay constant
but i when u say let Nzero = 100 and N = x im not sure where to plug them in at would it be:

-((ln(x/100)/k)) = T ?



Andrew/utramos/???
Let me start over a little. My first post and this post will give the same answer but this one should be a little easier to understand.
Let's start with 100 atoms of K40 many moons ago. That will decay to Ar40. We will call the final # atoms K40 as X and that is what we have today. That means Ar40 will be 100-X today.
So the ratio today is Ar/K = 1.55 as stated in the problem.
Substituting in the ratio we have
100-X/X = 1.55
Solve for X = 39.2 atoms K.
Ar = 100-X = 60.7.
You can check the ratio here to make sure it is ok. That would be 60.7/39.2 = 1.55
You have determined k = 0.693/half life and I obtained 5.42 x 10^-10 years^-1.

So we start with 100 atoms K many moons ago and today we have 39.2. Therefore, No = number of K atoms initially = 100 and N = number of K atoms today = 39.2. Plug that into the decay equation.
ln(No/N) = kt
ln(100/39.2) = 5.42 x 10^-10 t
solve for t. I get something like 10^9 years.
In your second question you asked if the following was correct.
-((ln(x/100)/k)) = T ?
I don't think so. I think it should be as I have it above.
I hope this helps. Repost if you still have a question about what I have done.


I think i am just not sure on how u got this

Solve for X = 39.2 atoms K.
Ar = 100-X = 60.7.


Actually, it doesn't matter what the Ar is because you are using No/N for K and using 100 for No, which we started with, and 39.2 for N (for K) for when it finished decaying (that's what we calculated N to be). However, the 60.7 for Ar comes from this:
If we started with 100 atoms K40, it decays over the ages and ends up X (which we later determined X to be 39.2). So if Ar is 100-X, then 100-39.2 = 60.7. OK? or not?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math/Radioactive Dating

    My teacher said that if the ratio of mass (in a rock) for 40K and 40Ar was 1:3 then the age of the rock would be 2.5 billion years. I don't understand how he concluded that to be the age. The only thing he knew was that the half-life …
  2. College Chemistry

    A rock containing 238U and 206Pb was examined to determine its appropriate age. The molar ratio of 206Pb to 238U was 0.1462. Assuming no lead was originally present and that all lead formed remained in the rock. What is the age of …
  3. Chemistry

    A rock containing 238U and 206Pb was examined to determine its appropriate age. The molar ratio of 206Pb to 238U was 0.1462. Assuming no lead was originally present and that all lead formed remained in the rock. What is the age of …
  4. earth space science

    Potassium-40 has a half-life of approximately 1.25 billion years. Approximately how many years will pass before a sample of potassium-40 contains one-sixteenth the original amount of parent isotope?
  5. Earth Science

    Why is potassium-argon dating most applicable to dating very old rocks?
  6. Math in Science

    A rock containing a newly discovered fossil is found to contain 5 mg of an unstable form of potassium and 5 mg of the stable element formed from its decay. If the half-life of the unstable form of potassium is 1.3 billion years, how …
  7. 8th Grade Earth Science Help?

    Which of the following terms refers to the time it takes for one-half of the radioactive atoms in a sample of a radioactive element to decay?
  8. Physics - Half Life Question Check!!!

    An ancient rock is found to contain 40Ar gas, indicating that 77% of the 40K in the rock has decayed since the rock solidified. Any argon would have boiled out of liquid rock. How long ago did the rock solidify?
  9. astronomy

    The isotope potassium-40 (40K) decays into the isotope argon-40 (40Ar) with a half-life of 1.25 billion years. Suppose we find a rock in which seven-eighths of the potassium-40 has decayed to become argon-40, and only one-eighth of …
  10. science

    Potassium-40 has a half life of 1.2 billion years and decays into the stable daughter isotope Argon-40. If you find a rock that contains 20 Potassium-40 atoms and 60 Argon-40 atoms, how old is the rock?

More Similar Questions

Post a New Question