Answer:
(1) Z = 82, M = 208; Â (2) Â Z = 82, M = 208
Step-by-step explanation:
(1) Decay of Th-232
The unbalanced nuclear equation is
[tex]_{90}^{232}\text{Th} \longrightarrow _{x}^{y}\text{Z} +6 _{2}^{4}\text{He} + 4 _{-1}^{0}\text{e}[/tex]
The main point to remember in balancing nuclear equations is that the sums of the superscripts and the subscripts must be the same on each side of the equation. Â
Then
 90 = x + 6×2 + 4(-1), so x =  90 – 12 + 4 =  82
232 = y + 6×4 + 4×0,  so y = 232 – 24    = 208
Z = 82, M = 208
(2) Decay of U-238
The unbalanced nuclear equation is
[tex]_{92}^{238}\text{U} \longrightarrow _{x}^{y}\text{Z} +6 _{2}^{4}\text{He} + 2 _{-1}^{0}\text{e}[/tex]
Then
 92 = x + 6×2 + 2(-1), so x =  92 – 12 + 2 =  82
238 = y + 6×4 +4×0,   so y = 238 – 24   = 214
Z = 82, M = 214
