# Half life

1. Sep 20, 2010

### quantum_enhan

1. The problem statement, all variables and given/known data

The half-life of radioactive carbon 14 is 5700 years. After a plant or animal dies, the level of carbon 14 decreases as the
adioactive carbon disintegrates. The decay of radioactive material is given by the relationship A = A0e^(-kt), where A0 is the initial amount of material at time 0 and t represents the time measured from time 0 in years. For carbon 14, k = 1.216 × 10-4 years^-1. Samples from an Egyptian mummy show that the carbon 14 level is one-third that found in the atmosphere. Determine the approximate age of the mummy.

2. Relevant equations

A = A0e^(-kt),

3. The attempt at a solution

I didnt really know what I should do with this, but heres what I did:
A=A0e^(-kt)
where A=1/3A0 ?
1/3A0=A0e^(-kt)
1/3=e^(-kt)
ln 1 - ln 3 = -kt
t = (-ln 1 + ln 3)/k

2. Sep 20, 2010

### ehild

It looks all right what you did. The living being exchanges carbon with its surroundings, and from the built-in carbon in the body the ratio of C14 was the same as in the atmosphere. The exchange has ceased since death. Supposing this ratio of C14 in the atmosphere did not change during ten thousand years, A0 is equal to the present ratio.

ehild

3. Sep 20, 2010

### epenguin

Yes that is OK - but you need to answer the question - what is t for the mummy?

Data given in the question enables you to calculate k.

You calculator will give you ln 1. But first think, you should know it yourself - get it from the meaning of ln.