# How do you calculate the half life of carbon 14?

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#### Explanation

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A quick way to calculate Half-Life is to use the expression:

Where

1.21 x

So

Let me know if you would like the derivation of this.

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#### Explanation

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So to find the half life of carbon 14...

To start, let's have some facts that one should know:

- The half life of any element is the amount of time it takes to lose half the amount of it's weight
- Carbon 14 dating is finding out how old an artifact is by figuring out much carbon is left in it.
- Carbon's half life is 5730 years for
**ONE**half life - The validity of the method stops after 30,000 years

Okay now that you know a little bit more information, you can try to find out how much carbon is in element.

So given that the half-life of carbon-14 is 5730 years, consider a sample of fossilized wood that, when alive would have contained 24 g of carbon-14. It now contains 1.5 g of carbon-14. How old is the sample?

You can divide 24 by 2 until you get 1.5 g. Why? Because during each half-life, carbon loses half of its weight. So...

Remember to keep track of the number of half-lives you have. In this case there are 4 half-lives. In each of these half-lives, 5730 have passed so you times 5730 by 4.

There's your answer. It took 22,920 years for 24 g to decay to 1.5 g

I hoped this helped!

Source of Question: A practice problem from my teacher

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