Consider an initially pure sample of radioactive material products are themselves radioactive with differing half$-$lives. equations characterizing the concentration of various isotop decay chain is of the form $1->2->3->4->...$ N$.$ Solve this set o fashion for the isotopic concentrations N$($t$),$ N$($t$),...$ In p long$-$time composition of the sample if the half$-$life of one of t longer than those characterizing other isotopes in the chain.Consider an initially pure sample of radioactive material whose successive decay

products are themselves radioactive with differing half$-$lives. Write the isotopic rate

equations characterizing the concentration of various isotopes in the sample if the

decay chain is of the form $1234$dotsN. Solve this set of equations in a stepwise

fashion for the isotopic concentrations $N_1(t),N_2(t),$dots In particular, determine the

long$-$time composition of the sample if the half$-$life of one of the isotopes is very much

longer than those characterizing other isotopes in the chain.