Question

The ratio of 14C to 12C in living organisms is 1.3 × 10-12. The fossilized remains of an organism are discovered and the ratio of 14C to 12C in the fossil is measured to be 3.1 × 10-13. How long ago, in years was the organism alive? (The half life of 14C is 5,730 years.)

Answer 1

Answer:

11,850 years ago.

Explanation:

Given:The ratio of 14C to 12C in living organisms = 1.3 × 10⁻¹²

the ratio of 14C to 12C in the fossil is measured to be 3.1 × 10⁻¹³

3.1 × 10⁻¹³ = 1.3 × 10⁻¹² $(1/2)^{{t}/{5730}}$

⇒ 3.1 × 10⁻¹³ / 1.3 × 10⁻¹² =  $(1/2)^{{t}/{5730}}$

⇒ t  / 5730 = [ ln ( 3.1 × 10⁻¹³ / 1.3 × 10⁻¹²) ] / ln(0.5)

⇒ t = 11850 years