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Can someone check my Radiometric Dating Problems?

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Can someone check my Radiometric Dating Problems?

Postby QuantumMoron » Sun Jan 24, 2010 12:10 am

1. The half like of carbon 14 is 5730 years. Some charcoal from an ancient village has only 1/16 of its original level of carbon 14. How old is the charcoal? My answer was 45,840 yrs.

2. The half life of potassium 40 is 1.3 billion years. How much of that potassium 40 would have decayed to argon after 3.9 billion years? My answer was 3/8.
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Postby mith » Sun Jan 24, 2010 5:01 am

2. 3.9 is more than 1.3 so wouldn't that mean at least half of it was decayed?
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Postby Chroma » Sun Jan 24, 2010 6:11 am

For Question #1:
I might be over simplifying it, but 1/16 is 4 half life periods (1/2 * 1/2 * 1/2 * 1/2 = 1/16)
So 4 * 5730 years = 22,920 years

For Question #2:
3.9 / 1.3 = 3 Half-life periods so: 1/2 *1/2 * 1/2 = 1/8 of the potassium would remain. 1 - 1/8 = 7/8 of the potassium would have decayed to argon.
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Postby mith » Sun Jan 24, 2010 5:18 pm

You can just use exponents if you don't want to halve many times

i.e. (.5)^(n/half life) where n is number of years in question
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Postby Chroma » Sun Jan 24, 2010 7:26 pm

I knew there was a way to do it using exponents...

1/16 = (1/2)^(n/5730)
ln(1/16) = ln((1/2)^(n/5730))
ln(1/16) = (n/5730) * ln(1/2)
n/5730 = ln(1/16) / ln(1/2) = 4
n = 5730 * 4 = 22,920
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Re: Can someone check my Radiometric Dating Problems?

Postby QuantumMoron » Sun Jan 24, 2010 11:58 pm

Thanks for the help everyone
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