a) Alvin:
²³⁵U (α, t_½ = 7.04 × 10⁸ y) (fissile @ spherical critical diameter 17.3 cm) →
²³¹Th (β⁻, t_½ = 25.5 h) →
²³¹Pa (α, t_½ = 3.27 × 10⁴ y) →
²²⁷Ac (β⁻, t_½ = 21.8 y) →
²²⁷Th (α, t_½ = 18.7 d) →
²²³Ra (α, t_½ = 11.4 d) →
²¹⁹Rn (α, t_½ = 3.96 s) →
²¹⁵Po (α, t_½ = 1.78 s) →
²¹¹Pb (β⁻, t_½ = 36.1 min) →
²¹¹Bi (α, t_½ = 2.14 min) →
²⁰⁷Tl (β⁻, t_½ = 4.77 min) →
²⁰⁷Pb (stable)

b) Theodore:
²³⁹Pu (α, t_½ = 2.031 × 10⁴ y) →
²³⁵U (α, t_½ = 7.04 × 10⁸ y) →
²³¹Th (β⁻, t_½ = 25.5 h) →
²³¹Pa (α, t_½ = 3.27 × 10⁴ y) →
²²⁷Ac (β⁻, t_½ = 21.8 y) →
²²⁷Th (α, t_½ = 18.7 d) →
²²³Ra (α, t_½ = 11.4 d) →
²¹⁹Rn (α, t_½ = 3.96 s) →
²¹⁵Po (α, t_½ = 1.78 s) →
²¹¹Pb (β⁻, t_½ = 36.1 min) →
²¹¹Bi (α, t_½ = 2.14 min) →
²⁰⁷Tl (β⁻, t_½ = 4.77 min) →
²⁰⁷Pb (stable)

c) Simon:
²²⁵Ra (β⁻, t_½ = 14.9 d) →
²²⁵Ac (α, t_½ = 9.92 d) →
²²¹Fr (α, t_½ = 4.18 min) →
²¹⁷At (α, t_½ = 32.3 ms) →
²¹³Bi (β⁻, t_½ = 45.6 min) →
²¹³Po (α, t_½ = 3.65 μs) →
²⁰⁹Pb (β⁻, t_½ = 3.25 h) →
²⁰⁹Bi (α, t_½ = 2.01 × 10¹⁹ y) (this is WAY more than the age of the universe so it’s unlikely that any atom in the sample will become tellurium in Simon’s lifetime)→
²⁰⁵Tl (stable)