Question

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it?11440 years1430 years4750 years2375 years4290 years

Answer 1

Answer: 11440 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)}=(2.303)/(k)\log(100)/(50)`

`t_{(1)/(2)}=(0.69)/(k)`

`5720years=(0.69)/(k)`

`(0.69)/(5720years)=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 decayed = 75

a - x = amount left after decay process = 100 - 75 = 25

`t=(2.303)/(1.2* 10^(-4))\log(100)/(25)`

`t=11440years`

Thus the piece of wood is 11440 years old.