The half-life for the radioactive decay of carbon-14 to nitrogen-14 is 5.73 x 10^3 years. Suppose nuclear chemical analysis shows that there is 0.523mmol of nitrogen-14 for every 1.000 mmol of carbon-14 in a certain sample of rock.
Calculate the age of the rock. Round your answer to 2 significant digits.

Answer : The time passed in years is

Explanation :

Half-life =

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 = initial amount of the reactant  = 1.000 mol

a - x = amount left after decay process = 1.000 - 0.532 = 0.468 mol

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

Therefore, the time passed in years is

its first and third is your answer i did the qustion the fourth isnt right