Question

The half-life of carbon-14 is 5,730 years. Suppose a fossil is found with 20 percent as much of its carbon-14 as compared to a living sample. How old is the fossil

Answer 1

Answer: 13,307 years

Step-by-step explanation: i got it right on the quiz/asignment

Answer 2

Answer: The sample is 13414 years old.

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= 100

a - x = amount left after decay process=
`(20)/(100)* 100=20`

a) for completion of half life:

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)/(5730)=0.00012years^(-1)`

b) for completion of 20% of reaction

`t=(2.303)/(0.00012)\log(100)/(20)`

`t=13414years`

The sample is 13414 years old.