Question

The radioactive 14C in living organisms results in an activity of 15.3 disintegrations per minute per gram (d/min·g) of carbon. If a piece of leather uncovered by an archeologist is measured to have 9.0 d/min·g, what is the approximate age of the leather? The half-life of 14C is 5730 years.

Answer 1

The half-life of a sample is the amount of time taken for the decay of 50% of the content of a material. The rate of decay is useful in determining the age of the material.

To solve the problem, follow the three steps given,

Step 1) Determination of the decimal fraction of 14C that is remaining:

Fraction of 14C remaining= Initial rate of disintegration/ Present rate of disintegration

9.00 / 15.3 = 0.588235

Step 2) Estimation of the number of half-lives have elapsed:

(1/2)n = Amount of 14C remaining

where n= number of half lives that have occurred.

> (1/2)n = 0.588235

> n log 0.5 = log 0.588235

> n x -0.3010= -0.230449

n = 0.7656

Step 3) Determination of time elapsed:

5730 yr x 0.7656 = 4386.95 years (approximately 4387 years)

Answer: The piece of leather is about 4387 years old.