Question

A piece of charcoal is found to contain

30% of the carbon 14 that it originally

had. When did the tree die from which the

charcoal came? use 5600 years as the

half-life of carbon 14.


A) 9709.46

B) 9708.33

C) 9708.34

D) 9709.45

Answer 1

Answer: The tree died 9709.46 years before.

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 = 100

a - x = amount left after decay process =
`(30)/(100)* 100=30`

a) to find 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)/(5600years)=1.24* 10^(-4)years^(-1)`

b) to know the age

`t=(2.303)/(1.24* 10^(-4))\log(100)/(30)`

`t=9709.46years`

The tree died 9709.46 years before.