Question

Suppose that a 6.5 gram of an element with a mass number 105 decays at a rate of 6.54*10^11 Bq. What is it’s half life in years?

Answer 1

The activity of a radioactive sample consisting of a single radioactive isotope is given by:

A = λ*N

where λ is the decay constant of the isotope and N is the number of atoms of the isotope in the sample.

The decay constant and halflife (T) of a radioactive isotope are related by:

λ = ln(2)/T

so,

A = ln(2)*N/T

Multiplying no.of moles by avagadro number to calculate atoms

6.5/105×avagadro no.=0.3728×10^23

T=3.728×10^22/6.54×10^11=5.7×10^10 sec=1807.55 years