Question

Compared with the fibers of cotton plants growing today, what is the relative ratio radioactivity in the old material vs the relative amount radioactivity in the new material? The half-life of 14C is 5730 y. (A0 = original radioactivity and At = current radioactivity).
For a quipu sample that is 4800 years old, we will calculate the ratio of 14C/12C in the sample.
At/A0 = ?

Answer 1

Answer:

0.56

Explanation:

From the formula;

0.693/t1/2 = 2.303/t log (Ao/At)

t1/2 = half life of the C-14 = 5730 y

t = time elapsed = 4800 y

At = Activity of C-14 at time t

Ao= Activity of a living C-14 sample

0.693/5730 = 2.303/4800 log (Ao/At)

1.2 * 10^-4 = 4.8 * 10^-4 log (Ao/At)

log (Ao/At) = 1.2 * 10^-4/4.8 * 10^-4

log (Ao/At) = 0.25

Ao/At = Antilog (0.25)

Ao/At = 1.778

Hence;

At/Ao = (1.778)^-1

At/Ao = 0.56