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_((1)/(2))# = #(0.693)/(lambda)#

Where #lambda# is the decay constant and has the value of

1.21 x #10^(-4) yr^(-1)#

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

#t_((1)/(2))# = 5.73 x #10^(3) yr#

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

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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...

#24/2 = 12# One half-life

#12/2 = 6# Second half-life

#6/2 = 3# Third half-life

#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 * 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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