Chapter 30, Problem 78GP

To determine

To show:Decay series classified into four family.

Explanation of Solution

The mass number changes only with $\alpha$ decay, and it changes by $-4.$ If the mass number is 4 n, then the new number is $4n-4=4(n-1)=4n^{\prime }.$ There is a similar result for each family, as shown here.

  $\begin{array}{l}4n\to 4n-4=4(n-1)=4n^{\prime }\hfill \\ 4n+1\to 4n-4+1=4(n-1)+1=4n^{\prime }+1\hfill \end{array}$

  $\begin{array}{l}4n+2\to 4n-4+2=4(n-1)+2=4n^{\prime }+2\hfill \\ 4n+3\to 4n-4+3=4(n-1)+3=4n^{\prime }+3\hfill \end{array}$

Therefore, the daughter nuclides are always in the same family.