Question

A fossil was analyzed and determined to have a carbon-14 level that is 70 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil? Express your answer with the appropriate units. View Available Hint(s) t t t = nothing nothing

Answer 1

Answer: 2948

Step-by-step explanation:

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=\frac{0.69}{t_{(1)/(2)}}=(0.693)/(5730)=1.21* 10^(-4)years^(-1)`

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

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

where,

k = rate constant =
`1.21* 10^(-4)years^(-1)`

t = age of sample = ?

a = let initial amount of the reactant = 100

a - x = amount left after decay process =
`(70)/(100)* 100=70`

`t=(2.303)/(1.21* 10^(-4))\log(100)/(70)`

`t=2948years`

Thus the fossil is 2948 years old.