Question

An old piece of wood has a carbon mass of 124 g and an activity of 13 Bq. How old is the song? The radioactive isotope of natural carbon has f = 1.3⋅10−12 parts and has a half life of 5730 years. The average for the year is 3.156⋅107 seconds. Please give your answer in years (ie a).

Answer 1

Activity R should be proportional to the number of radioactive nuclei, N, and inversely proportional to their half

life, t1/2.

R=(0.693*N) / t1/2

where N is the number of radioactive nuclei present, having half-life t1/2.

The half-life of a radioactive isotope describes the amount of time that it takes half of the isotope in a sample to

decay.

In the case of radiocarbon, the half-life of carbon 14 is 5,730 years. After 5,730 years, the amount of carbon 14 left

in the body is half of the original amount. If the amount of carbon 14 is halved every 5,730 years, it will not take

very long to reach an amount that is too small to analyze.  

t =[ ln ( N/N0 ) / (-0.693) ] * t1/2

Where t1/2  is the half-life of the isotope carbon 14, t is the age of the fossil (or the date of death), ln() is the natural

logarithm function, N is mass of radioactive material at time interval (t) and N0 is mass of the original amount of

radioactive material.