Question

Wood deposits recovered from an archaeological site contain 36% of the C-14 they originally contained. How long ago did the tree from which the wood was obtained die?

Answer 1

Answer: It was obtained 8515 years ago

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process

a) to find the rate constant:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

`t_{(1)/(2)}=(0.693)/(k)`

`k=(0.693)/(5760)=0.00012years^(-1)`

b) for completion of 36% of reaction

`t=(2.303)/(k)\log(100)/(36)`

`t=(2.303)/(0.00012)\log(100)/(36)`

t = 8515 years

The time was 8515 years.