How do you calculate half life of carbon 14?

1 Answer
Jan 14, 2016

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:

Nt=N0(12)tt12

or
Nt=N02tt12

or
Nt=N02tt12

Where
Nt is how much of the substance you have left at time t
N0 is how much you started with (at time 0)
t is how much time has elepsed, and
t12 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 Nt 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?

Nt=1kg25.61

Nt=0.020617kg

Calculating the half life from NtandN0 is a bit more complicated, because we are looking for a number inside an exponent. To do this, we need to use logarithms:

Nt=N02tt12

2tt12=N0Nt

log2(N0Nt)=tt12

t12=tlog2(N0Nt)

The formula is also frequently expressed using the natural logorithm:

t12=tln2ln(N0Nt)

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.