Asample contains 25% parent isotope and 75% daughter isotopes. if the half-life of the parent isotope is 72 years, how old is the sample?

The sample is 144 years old.

Explanation: This is a type of radioactive decay and all radioactive decays follow first order kinetics.

We are given half life which is 72 years.  

To calculate the rate constant, we use the formula:

Also 25 % of parent isotope is left, that means 75 % has been decomposed

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

where,

k = rate constant

t = time taken for decay process

a = initial amount of the reactant  = parent isotope= 100

a - x = amount left after decay process  = 25

Putting values in above equation, we get:

in the given question, the partial pressure is calculated by using the ideal gas equation, that is, pv = nrt

here, p is pressure, v is volume = 25 l, n is number of moles = 0.0104 moles, r is gas constant = -0.0821 l.atm / mol.k

t is temperature = 273 k

p = nrt / v

p = (0.0104 mol × 0.0821 l.atm / mol.k × 273 k) / 25 l

= 0.0093 atm

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