In 1991 a frozen body of an "Iceman" was found in the Italian Alps.The fraction of compared to found in the body's bones,hair,and leather clothing was 6.94 * 10^-13.The half-life of is 5,730 years and the ratio of to in living organisms is 1 to 7.41 *10¹¹.When did the Iceman die?

Question

Quizplus · Accepted Answer

We can use the equation for radioactive decay:
Nt = No(1/2)^(t/T)
where Nt is the final amount, No is the initial amount, t is the time elapsed, T is the half-life.
First, we need to find the initial ratio of 14C to 12C in the Iceman:
N(14C)/N(12C) = 6.94 x 10^-13
Assuming the ratio was the same in living organisms at the time of death, we can find the initial ratio of 14C to 12C:
N(14C)/N(12C) = 1/7.41 x 10^-10
Equating the two expressions for N(14C)/N(12C) and solving for t, we get:
t = (ln 6.94 x 10^-13) x (5730/ln 7.41 x 10^-10)
t = 5300 years
Therefore, the Iceman died 5500 years ago (adding 200 years for the time it took for him to freeze).

In 1991 a Frozen Body of an "Iceman" Was Found