Question

An archaeologist on a dig finds a fragment of an ancient basket woven from grass. Later, it is determined that the carbon-14 content of the grass in the basket is 8.33% that of an equal carbon sample from present-day grass. What is the age of the basket? Answer in years.

Answer 1

Half life of Carbon -14 = 5730 Years

Write the expression between half life time and decay constant.
? = ln 2 / T_1/2

= ln 2 / 5730
? = 1.21 * 10^-4 Years^-1
here T_1/2 is Half life of Carbon -14 and ? is Decay Constant.

Consider the following expression to calculate the age of basket .

Let age of basket is t.

N = No e -?t
Taking Log , and solve for t.

We get
t = -ln (N / No) / ?
Substitute N =( 8.33 /100 No)= 0.0833No in above equation.

t = - ln (0.0833)/ (1.21*10^-4)
t = 20539.7 Years

Age of basket is t = 20540 Years