Question

A sample has a Subscript 6 Superscript 14 Baseline Upper C activity of 0.0020 Bq per gram of carbon. (a) Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq. (b) Evidence suggests that the value of 0.23 Bq might have been as much as 37% larger. Repeat part (a), taking into account this 37% increase.

Answer 1

a) As per the decay law:

------------------------ (1)

A= activity of sample per gm = 0.0020 Bq

A0 = reference activity per gm = 0.23 Bq

= decay constant

t = sample age

For C14, with a half life of 5730 years, the decay constant is given as

therfore,

Substituting for A, A0 and lambda in eq 1 we get

taking ln on both sides and substituting the value of

t = 39, 215 years

b) Taking the 37% increase the value of = 0.23 * 1.37 = 0.315 Bq

Following the same steps as above we get:

t = 41,816 years