Question

This exercise uses the radioactive decay model The burial cloth of an Egyptian mummy is estimated to contain 60% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon- 14 is 5730 years. Round your answer to the nearest ten years.)

Answer 1

4257 years

Explanation:

Given that:

Half-life of carbon 14 (t1/2) = 5730

Estimated carbon 14 content = 60% of amount of carbon 14 = 0.6

Using the model :

m(t) = mo*e^-rt

Decay rate (r) = In2/t1/2 = 0.00012

mo = initial mass

Hence,

Mass of carbon 14 in mummy m(t) = 0.6mo

0.6mo = mo*e^-(0.00012 * t)

0.6 = e^-(0.00012 * t)

Take the ln of both sides

In(0.6) = - 0.00012t

−0.510825 = - 0.00012t

t = 0.510825 / 0.00012

t = 4256.875

t = 4257 (nearest whole number)