Question

The age of an ancient tree trunk is estimated using radiocarbon dating. If the trunk has a C-14 decay rate that is 34% of what it is in living plants, how old is the trunk? The half-life of C-14 is 5730 years.

Answer 1

Answer:

8923 years

Step-by-step explanation:

Half life of C-14 = 5730yrs

decay rate= 34%

Halt life (t^1/2) = (ln2) / k

5730 = (ln2) /k

k = (ln2) / 5730

k = 1.209 * 10^-4

For first order reaction in radioactivity,

ln(initial amount) = -kt

ln(34/100) = -(1.209*10^-4)t

-1.0788 = -(1.209*10^-4)t

t = -1.7088/ -1.209*10^-4

t = 8923 years