The carbon–14 activity in papyrus growing along the Nile River today is 231...

Question

The carbon–14 activity in papyrus growing along the Nile River today is 231 decay events per kilogram of carbon. If a papyrus scroll found in the ruins from ancient Egypt has a carbon–14 activity of 160  decay events per kilogram of carbon, how old is the scroll?

Answer 1

For a first order decay (radioactive decay), we can use the formula

FR = 0.5ⁿ

FR = fraction remaining = 160 / 231 = 0.6926

n = number of half lives that have elapsed = ?

0.6926 = 0.5ⁿ

log 0.6926 = log 0.5 n

-0.159 / -0.301 = n

n = 0.529 half lives have elapsed

Half life for C-14 = ~5400 yrs

Age of sample = 5400 yrs x 0.529 = ~2852 years