Question

The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 69.4​% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Answer 1

Answer: 9595.8 years

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=(0.693)/(5750)=1.2* 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

t = age of sample

a = let initial amount of the reactant =100

x = amount decomposed or lost =
`(69.4)/(100)* 100=69.4`

a - x = amount left after decay process= (100-69.4)= 30.6

Putting in the values:

`t=(2.303)/(1.2* 10^(-4))\log(100)/(30.6)`

`t=9595.8years`

Thus the bones were 9595.8 years old.