Question

The half-life of the carbon isotope C-14 is approximately 5,715 years. What percent of a given amount remains after 300 years? Round your answer to two decimal places.

Answer 1

Answer: 96.34%

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)/(5715)=0.00012years^(-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 = time for decomposition = 300 years

a = let initial amount of the reactant = 100

a - x = amount left after decay process = ?

`300=(2.303)/(0.00012)\log(100)/(100-x)`

`x=3.66`

`(a-x)=100-3.66=96.34`

Thus 96.34 percent of a given amount remains after 300 years.