Question

A 250-mg sample of carbon from wood underwent 15300 carbon-14 disintegrations in 36 hours. Estimate the time since the death of the sample.

Answer 1

The correct answer is - 9935 years approximately.

Step-by-step explanation:

Let z be the age in years to be found:

(15300 disintegrations) x (1.0 g / 0.250 g) / (1.84×10^4 disintegrations)

= 3.3260

half life of carbon = (1/2)^(z/5730 yr)

Solve for z

3.3260 = (1/2)^(z/5730)

Take the log of both sides:

log 3.3260 = (z/5730) log (1/2)

log 3.3260 / log (1/2) = z/5730

z = 5730 log 3.3260 / log (1/2)

= 1.73378816*5730

= 9935 years approximately.