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

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Michael Share
Nov 22, 2014

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

${t}_{\frac{1}{2}}$ = $\frac{0.693}{\lambda}$

Where $\lambda$ is the decay constant and has the value of

1.21 x ${10}^{- 4} y {r}^{- 1}$

So t_((1)/(2))=(0.693)/((1 .21).(10^(-4))

${t}_{\frac{1}{2}}$ = 5.73 x ${10}^{3} y r$

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

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4
Nov 21, 2014

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...

$\frac{24}{2} = 12$ One half-life

$\frac{12}{2} = 6$ Second half-life

$\frac{6}{2} = 3$ Third half-life

$\frac{3}{2} = 1.5$ Fourth half-life

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.

$5730 \cdot 4 = 22920$

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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