Percentage a material's carbon-14 has decayed?
I've been staring at this problem for hours and I'm not sure how to set it up. Any help would be great!
A sample of organic material has 18 g of carbon. The material is 23000 years old. Estimate what percentage of the material's carbon-14 has decayed.
Update:The answer provided is 93.8%
Comments
half-life of C-14 is 5,730 years
After 23,000 years, it undergoes 23,000 / 5,730 or
4.0139616056 half lives.
Ending Amount = Beginning Amount / 2^(n) where n = number of half lives.
Ending Amount = 1 / 2^4.0139616056
Ending Amount = 1 / 16.1555908074
Ending Amount = 0.0618980768 of the beginning amount
0.0618980768 x 100 =
6.18980768 per cent
Notice that the 18 grams isn't necessary for this calculation.
Half Life Calculator and Formulas are here:
http://www.1728.org/halflife.htm
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CORRECTION TO PREVIOUS CALCULATIONS
I had originally calculated how much C-14 is remaining. I should have calculated how much C-14 has decayed. No problem. Just subtract 6.18980768 per cent from 100% and you have:
93.81019232 %