Question

How do you calculate half life of carbon 14?

Answer 1

You can calculate half life if you know how much of the substance is left after a certain time, though typically it works the other way - the half life is known, and used to calculate age.

Explanation:

The formula for half life calculations is:

`N_t=N_0(1/2)^(t/t_(1/2))`

or
`N_t=N_0/2^(t/t_(1/2)`

or
`N_t=N_0 *2^(-t/t_(1/2)`

Where
`N_t` is how much of the substance you have left at time `t`
`N_0` is how much you started with (at time 0)
`t` is how much time has elepsed, and
`t_(1/2)` is the half life of the substance.

Half life is defined as the time after which half of a sample of a radioactive material will have decayed. In other words, if you start with 1 kg of material with a half life of 1 year, then after 1 year you will have 500g. After another year you will have half of that, or 250 g. After another year, you will have 125 g, and so on.

Calculating `N_t` is fairly straightforward. If, for example, we have the same 1kg sample of material with a half life of 1 year, how much do we have after 5.6 years?

`N_t=(1kg)/2^(5.6/1)`

`N_t = 0.020617 kg`

Calculating the half life from `N_t and N_0` is a bit more complicated, because we are looking for a number inside an exponent. To do this, we need to use logarithms:

`N_t=N_0/2^(t/t_(1/2)`

`2^(t/t_(1/2))=N_0/N_t`

`log_2(N_0/N_t)=t/t_(1/2)`

`t_(1/2) = t/log_2(N_0/N_t)`

The formula is also frequently expressed using the natural logorithm:

`t_(1/2) = (t*ln2)/ln(N_0/N_t)`

So, to answer the question, in order to calculate the half life of `""^14C` we would need to know three things: how much we started with, how much we finished with, and how much time had elapsed, then we just plug those values into the formula, and solve using a calculator.

If, however, your goal is to determine the half life of carbon so you can use it to determine an age, then Google is your friend:
5730 years.