Answer
See answers.
Work Step by Step
See Figure 30-11. The mass number A can only change by “-4”, when an $\alpha$ particle is emitted.
If the parent nucleus has a mass number of the form 4n, and its mass number decreases by exactly 4, the daughter’s mass number also belongs to the 4n family.
$$4n\rightarrow4n-4 = 4(n-1) = 4n’$$
Similar statements can be made for each of the other families.
$$4n+1\rightarrow4n+1-4 = 4(n-1)+1 = 4n’+1$$
$$4n+2\rightarrow4n+2-4 = 4(n-1)+2 = 4n’+2$$
$$4n+3\rightarrow4n+3-4 = 4(n-1)+3 = 4n’+3$$
All of the daughters belong to the same family.
