Question

Living matter has a carbon-14 activity of about 24.0 counts/min per gram of carbon. What is the age of an artifact for which the carbon-14 activity is 3.00 counts/min per gram of carbon? The half-life of carbon-14 is 5730 years. Express your answer with the appropriate units. I MÅ R O 2 ? Age = yr Age = 34380 Submit Submit Previous Answers Request Answer

Answer 1

Given:

Half life = 5730 years

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(5730)

= 1.209*10^-4 years-1

we have:

[C]o = 24

[C] = 3

k = 1.209*10^-4 years-1

use integrated rate law for 1st order reaction

ln[C] = ln[C]o - k*t

ln(3) = ln(24) - 1.209*10^-4*t

1.099 = 3.178 - 1.209*10^-4*t

1.209*10^-4*t = 2.079

t = 1.719*10^4 years

Answer: 1.72*10^4 years