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

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asked Jun 28, 2022 85.1k views

2 Answers

Martijn Laarman · Answer 1 · 2022-07-03T09:16:39+0000

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.