this post was submitted on 23 Nov 2023
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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)
From the half-lives and atomic masses (the little numbers that determine how many grams a mole weighs), they can calculate the specific activity of each sample.
Yeah, Simon's sample is 600000x more active than Theodore’s, which is a further 3000x more active than Alvin’s. Even though Simon’s sample produces mostly β particles (which are generally about 10 times less destructive), he is clearly the worst here.
Multiply that by the number of grams in the sample and you get the activity of each sample in becquerels.
Now just use a chipmunk body model and estimated distance from each sample to calculate the absorbed dose in grays (not to be confused with equivalent dose measured in sieverts). 70% lethal dose over 30 days is 10~12 Gy for mice so chipmunks should have it similar but take into account that they weigh around 100 g.
Also Ra is a gas which makes it even worse, becasue it easier gets in ur body.
Ra is a solid (Radium) Rn is a gas (Radon).
Unless I'm wrong. Id better check.
Nah, i fucked up
Good point. I compleely forgot chemical properties here.