a) Alvin:
²³⁵U (α, t½ = 7.04 × 10⁸ y) (fissile @ spherical critical diameter 17.3 cm) →
²³¹Th (β⁻, t½ = 25.5 h) →
²³¹Pa (α, t½ = 3.27 × 10⁴ y) →
²²⁷Ac (β⁻, t½ = 21.8 y) →
²²⁷Th (α, t½ = 18.7 d) →
²²³Ra (α, t½ = 11.4 d) →
²¹⁹Rn (α, t½ = 3.96 s) →
²¹⁵Po (α, t½ = 1.78 s) →
²¹¹Pb (β⁻, t½ = 36.1 min) →
²¹¹Bi (α, t½ = 2.14 min) →
²⁰⁷Tl (β⁻, t½ = 4.77 min) →
²⁰⁷Pb (stable)b) Theodore:
²³⁹Pu (α, t½ = 2.031 × 10⁴ y) →
²³⁵U (α, t½ = 7.04 × 10⁸ y) →
²³¹Th (β⁻, t½ = 25.5 h) →
²³¹Pa (α, t½ = 3.27 × 10⁴ y) →
²²⁷Ac (β⁻, t½ = 21.8 y) →
²²⁷Th (α, t½ = 18.7 d) →
²²³Ra (α, t½ = 11.4 d) →
²¹⁹Rn (α, t½ = 3.96 s) →
²¹⁵Po (α, t½ = 1.78 s) →
²¹¹Pb (β⁻, t½ = 36.1 min) →
²¹¹Bi (α, t½ = 2.14 min) →
²⁰⁷Tl (β⁻, t½ = 4.77 min) →
²⁰⁷Pb (stable)c) Simon:
²²⁵Ra (β⁻, t½ = 14.9 d) →
²²⁵Ac (α, t½ = 9.92 d) →
²²¹Fr (α, t½ = 4.18 min) →
²¹⁷At (α, t½ = 32.3 ms) →
²¹³Bi (β⁻, t½ = 45.6 min) →
²¹³Po (α, t½ = 3.65 μs) →
²⁰⁹Pb (β⁻, t½ = 3.25 h) →
²⁰⁹Bi (α, t½ = 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)So? Who is it?
Radium produces the most radiation by miles. The plutonium gives off some alpha radiation that won’t hurt you if you don’t eat it. (Eye protection would be a good idea I suppose.) I don’t remember what U-235 emits but I don’t think it’s a huge amount.
The half-life of 235U is hundreds of millions of years so it is not a concern. However, it will literally become a nuke if too much (a few liters or 60 kg) get too close together.
The half-life of plutonium-239 is tens of thousands of years so only a thousandth will get a chance to hurt Theodore over his lifetime. However, it is probably chemically toxic so it might cause non-radiation poisoning.
Radium-225 will decay in days, and will quickly go through 7 more radioactive reactions, both alpha and beta, before becoming essentially stable bismuth. It is the worst by far.
Definitely Simon since radium has a much higher activity than the other two.
Yes, you happen to be correct but you can’t just say that. Different isotopes of each of these elements can be many orders of magnitude more active. If I could summon a few grams of any isotope of carbon (like C-20 that decays in microseconds), I could kill you with radiation poisoning instantly.
Anyway, it’s β⁻ decay so they are all affected, plus some α from secondary products that will be mostly received by Simon.
Unless Alvin’s ²³⁵U is above critical mass, in which case they all die very quickly.
Your comment above gave the half lives of the main substances and their secondary products, right? Could you recommend any resources for someone to learn how to do what you did above?
I used nothing but about 20 Wikipedia pages lol. It would be more if I also checked the less common decay path but that’s <2% at most.
