The half-life for the α decay of uranium is 4.47 × 109 yr. determine the age (in years) of a rock specimen that contains 55.5% of its original number of atoms.

Explanation:

Half-life of uranium = years

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

Now we have to calculate the age of the sample:

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

where,

k = rate constant  =

t = age of sample  = ?

a = let initial amount of the reactant  = 100

a - x = amount left after decay process  =

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

Thus the age of a rock specimen that contains 55.5% of its original number of atoms is

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