How can the half-life of Carbon-14 help determine the age of organic materials?

[ConcealedDreamer]

The half-life of carbon-14 is 5730 years. If a sample had 26 g of carbon-14, how much would it contain after 22,920 years (x 4)?

 

[gerben]

calculate how many times the half-life time has past, you apparentely did so and that is 4 times, so that means that the original amount has halved 4 times...

after 1 time the half-life time you have half of the original amount
after 2 times the half-life time you have half of the half of the original amount so a quart
after 3 times...

 

[ConcealedDreamer]

I did 26 divided by 4, does that work? Or do I keep halving it? As in 1.625?

 

[gerben]

No if it halves 4 times, that does not mean yoiu have to divide by 4

take for example 20 to start with,
if you half that ones you have 10
if you halve it a second time you have 5
so after halving it two times you have what you had originally divided by 4

you have to keep halving, four times.
1/2 *1/2 *1/2 *1/2 = 1/16
so you have to divide by 16

 

[Ouabache]

Since biology is a subdiscipline of physics, and since we are in the physics forum. Here is another way to look at your question.
Radioactive decay of Carbon-14 follows an exponential decaying function of the form $$Ae^{-kt}$$

Carbon-14 follows the expontial decay: $$Q= Q_0 e^{-0.000121t}$$
where $$t$$ - years, $$Q_0$$ - initial mass, $$Q$$ - final mass.

So try that, plug in 26g for $$Q_0$$ and 22,920 years for $$t$$,
what do you get?

Ask you teacher/professor: Knowing the half-life of Carbon-14, how can that be used to calculate the age of dinosaur bones or other organic matter?