Calculating the Age of 1.4g of Charcoal Using Beta Decay

In summary, the 1.4g sample of old charcoal produces 0.7 beta decays per minute. It is approximately 8.904x1010 years old.
  • #1
QuarksAbove
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Homework Statement


Suppose you have a 1.4g sample of old charcoal. It produces 0.7 beta decays per minute. How old is the charcoal.

Given:
1g of carbon current day has 6.36x1010 atoms of 14C


Homework Equations



N = Noe-rt

N = number of atoms in the sample (current-day)
No = original number of atoms (i.e. at time of death)
r = decay rate = 1.21x10-4
t = time

The Attempt at a Solution



I know that No = 1.4*6.36x1010 = 8.904x1010
r = 1.21x10-4

what I don't understand is what to do with the 0.7 decays per minute. I know I need to solve for N before I can solve for t, but I'm stuck. As soon as I solve for N, it's plug and chug.

Any help would be much appreciated!
 
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  • #2
It would be helpful to know the units of the decay rate r.
 
  • #3
If you have N C14 atoms, how many of them decays in unit time? How is it related to the decay rate?

ehild
 
  • #4
SteamKing said:
It would be helpful to know the units of the decay rate r.

r = 1.21x10-4 /year


echild said:
If you have N C14 atoms, how many of them decays in unit time? How is it related to the decay rate?

If I have N C-14 atoms, then 0.7 of those N atoms decay each minute.. 0.7 decay/minute = 367920 atom decays per year.

I'm not sure how it's related to the decay rate. Sorry, I haven't done a problem with two rates before and it's really confusing.
 
  • #5
N is the number of the 14C atoms in the sample at present. N0 was the number of atoms when the sample got isolated. N=N0e-rt, so dN/dt=-rN0e-rt=-rN.

rN atoms decays in a year, that is about 368000 in the 1.4 g sample. You know r. What is N then?
Originally there were 6.36x1010atoms of 14C in 1 g sample. Current-day means "fresh" sample, which can interact with the surroundings, so has supply of 14C. The charcoal is isolated, so the number of 14C atom decreases with time.

ehild
 

1. How is the age of 1.4g of charcoal calculated using beta decay?

The age of 1.4g of charcoal can be calculated using the ratio of carbon-14 to carbon-12 in the sample. As carbon-14 is a radioactive isotope with a known half-life of 5,730 years, the amount of carbon-14 left in the sample can be used to determine its age.

2. What is beta decay and how does it relate to carbon-14 dating?

Beta decay is a type of radioactive decay in which an unstable atom releases a beta particle (an electron or positron) to become a more stable atom. Carbon-14 dating uses the rate of beta decay of the radioactive isotope carbon-14 to determine the age of organic materials.

3. Can other materials besides charcoal be dated using beta decay?

Yes, beta decay can be used to date any organic material that contains carbon, as long as it is less than 50,000 years old. This includes materials like wood, bone, and shell.

4. How accurate is beta decay in determining the age of 1.4g of charcoal?

Beta decay is a highly accurate method of dating, with a margin of error of only a few years. However, the accuracy can be affected by factors such as contamination or the presence of other radioactive isotopes in the sample.

5. Are there any limitations to using beta decay to calculate the age of 1.4g of charcoal?

One limitation of using beta decay is that it can only be used to date materials that contain organic carbon. Additionally, the method is only accurate for samples that are less than 50,000 years old, as beyond this point, the amount of carbon-14 left in the sample is too small to accurately measure.

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