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.
Copy this into a new comment and we’ll call it even.
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.
Are these decay rates specified for isolated atoms?
I believe they would decay faster when bombarded by particles from fellow atoms, no? So we'd have to account for the mass, shape and density of the samples to get true rates. I don't think that would change the rankings, but it might increase Simon's troubles if the radon was frozen or otherwise really compressed, for example.
Probably yes. But I don't think that major reactions would ensue in such quantities of several grams – after all, nuclei are pretty sparse so most radiation would just escape and hit one of the chipmunks or something else. It takes many kilograms of concentrated ²³⁵U to start a runaway fission.
Something something half-life decay funny particles radiation you are dead
As I understand it Alvin and Theodore should be fine but Simon is fucked.
I mean, they are like 10 centimeters from each other. They are all dead
It is the disintegration chain of each atom and the particules and half life of all.
Half life is the time it takes for half the atoms to disintegrate. The first letter is the emited radiation (alpha, beta, gamma).
You can derived how dangerous each of these materials is from these informations.
On a quick glance, radium should be the deadliest one, because the half lives are all very short, so that's a lot of deadly radiations. On the other hand, uranium is said to be on a critical mass, which could be a chain reaction.
I didn't say it was anywhere close to critical mass. People were suggesting Alvin's sample would be worst (likely because of how U-235 is notoriously used in nukes) but I reminded them that only a big chunk of sufficiently pure U-235 would be catastrophic, otherwise the radiation is surprisingly mild.
And Theodore’s sample will also contain a varying amount of U-235 but it will take tens of thousands of years to get pure enough.