Question

Question 4 0.83 pts A sample of the inner part of a redwood tree felled in 1874 was shown to have 14C activity of 10.93 dpm/g. Calculate the approximate age of the tree when it was cut down. Compare this age with that obtained from tree ring data, which estimated that the tree began to grow in 979 52 B.C. Use 13.4 dpm/g for the value of Ao. t1/2 of 14C = 5730 years (Round your answer to a whole number)

Answer 1

The fraction of activity A remaining after n half-lives is given by:

$A = \frac{A_{0}}{2^{n}}$

where n = number of half lives passed

A₀ = initial activity.

Given,

A₀ = 13.4 dpm/g

A = 10.93 dpm/g

so number of half lives passed =

Ао 21 Ао >n=log(2) n = 1 0.693 13.4 In( 10.93 0.29394 A

Age = thus the time passed = n * T_1/2 = 0.29394 * 5730 = 1684 years (approx)

(The age calculated by ring data ranges from 2801-2905 years which is very different than half life age calculation)