Answer to Question #143066 in General Chemistry for Jushoa

Question

The charred bones of a sloth in a cave in Chile represents the earliest evidence human presence at the southern tip of south america. A sample of the bone has a specific activity of 5.22 disintegrations per minute per gram of carbon (d/min*g. If tge ratio of 12C: 14C in living organisms result in a specific activity of 15.3 d/min*g, how old are the bone (t1/2 of 14C = 5730 yr?

Answer 1

A = A₀ (1/2)ⁿ

A = 5.22

A₀ = 15.3

5.22 = 15.3 (1/2)ⁿ

n = 1.55 half-lives

5730 x 1.55 = 8881.5 years