Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

Question

Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire.

Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

I have already tried the answer of 5600 ln(0.02) / ln(0.5). I am not sure why that is incorrect if someone knows where I am going wrong that would be very helpful.

Answer 1

Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire.

Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

I have already tried the answer of 5600 ln(0.02) / ln(0.5). I am not sure why that is incorrect if someone knows where I am going wrong that would be very helpful.

Hello Katherine,

Let us see...

t_1/2 = 5600 yr

A_r = 2 % (amount remaining)

Find the age?

Using:

Ar = Ao(1/2)^{[time / half life time t 1/2]}

Solve for time knowing that A_r = 2 % or 0.02 and A_o = 1

0.02 = 1(1/2)^{[t / 5600]}

Ln(0.02) = [t / 5600] * Ln(1/2)

Ln(0.02)/Ln(1/2) = t / 5600

5600 * [Ln(0.02)/Ln(1/2)] = t

t = 31,605 years

The age of the specimen is 31,650 years.