Calculating Age of Fossil Using 14C/12C Ratio

[element1945]

Homework Statement

Determine how old is a fossile where a 14C/12C ratio of 6.1 x 10^-13 is measured. 14C desintegration has a half-life of 5760 +- 40 years and proportion 14C/12C in living tissue is 1.17 x 10^-12. Determine the error in your calculation.

Homework Equations

Radioactive decay equation N=N0 exp(-kt/T)

The Attempt at a Solution

If N0= 1.17x10^-12
N = 6.1x10^-13
k= 0.693
T = 5800 or 5720

Solving in the equation gives

t= 5451 years for 5800 half-life and
t= 5376 years for 5720 half-life.

But inst supposed to be more years than the half-life of 14C?
I don't understand please help me.

 

[Borek]

But inst supposed to be more years than the half-life of 14C?

Why? Please elaborate.

What percentage of the original ¹⁴C is left in the sample?

 

[element1945]

Ok in the problem there's no data for 14C left in the sample. the only facts are the ratio in the sample: 6.1x10^-13, and the ratio of a living tissue: 1.17x10^-12. how to i calculate the 14C left in the sample? and there's the half-life...there are no other facts :(

 

[element1945]

do the ages that i calculate are correct?

 

[Borek]

Imagine you have 1 mole of carbon in the sample. From given ratios, how many moles of ¹⁴C should be present in this amount of carbon in living tissue? How many moles will be present in the 1 mole of carbon from the fossil?

Ages look OK, although you have probably used rounded down k for calculations, thus my results are about a 1 or 2 years higher.

 

[element1945]

The moles of 14C in the living tissue are

(1.17 atoms 14C / 6.023x10^23 atoms) x 1 mol = 1.94x10^-24 mol

I am correct?

 

[epenguin]

The moles of 14C in the living tissue are

(1.17 atoms 14C / 6.023x10^23 atoms) x 1 mol = 1.94x10^-24 mol

I am correct?

Wrong track - Avogadro number etc. irrelevant. You are given what something - it almost doesn't matter what it is - is now i.e. starts off as, what it has decayed to in a sample, and the time it takes it to decay to half what of whatever it started as. At least a ballpark for the object's age you should be able to tell us straight off. Tell us. It might jog you mind for what you have to do for more refined calculation.

 

[Borek]

Wrong track - Avogadro number etc. irrelevant.

While it is irrelevant, starting with known quantity often helps to understand what is going on. In the end Avogadro number will cancel out, but for many beginners it is much easier to compare well defined amounts of substance, than some abstract percentages and/or proportions.

Still, element1945 - you are wrong. You are told that

$$\frac {number of ^{14}C atoms} {number of ^{12}C atoms} = 1.17*10^{-12}$$