The half-life of an isotope with a very long half-life cannot be measured by observing its activity as a function of time, since the variation in activity over any reasonable time interval would be too small to be observed. Let m be the mass in grams of a given isotope of long half-life.
a. Show that the number of nuclei present in this quantity is N0=μmNA where μ is the molar mass of the isotope in g mol−1 and NA is the Avogadro constant.
b. From A=N0λe−λt show that the initial activity is A0=μmNAλ and hence that the half-life can be determined by measuring the initial activity (in Bq) and the mass of the sample (in grams).