Carbon-14 is a radioactive isotope that decays according to first-order kinetics in a process that has a half-life of 5730 years. if a sample containing carbon-14 now has 71% of its original concentration of carbon-14, how much time has passed in years? 4.09 ~ 103 years 5.73 x 103 years 2.38 x 103 years 2.83 x 103 years 3.52 * 104 years

Answer : The time passed in years is

Explanation :

Half-life = 5730 years

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  =

t = time passed by the sample  = ?

a = let initial amount of the reactant  = X g

a - x = amount left after decay process =

Now put all the given values in above equation, we get

Therefore, the time passed in years is

the answer is symmetrical : )