Carbon-14, which is present in all living tissue, radioactively decays via a first-order process. a one-gram sample of wood taken from a living tree gives a rate for carbon-14 decay of 13.6 counts per minute. if the half-life for carbon-14 is 5720 years, how old is a wood sample that gives a rate for carbon-14 decay of 4.4 counts per minute?

Answer : The age of sample is

Explanation :

Half-life = 5720 years

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

Now we have to calculate the age of sample.

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

where,

k = rate constant  =

t = age of the sample  = ?

a = let initial amount of the reactant  = 13.6 counts per min

a - x = amount left after decay process = 4.4 counts per min

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

Therefore, the age of sample is

the answer is a)

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