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)
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.
- ²³⁵U: 7.99 × 10⁴ Bq/g
- ²³⁹Pu: 2.29 × 10⁹ Bq/g
- ²²⁵Ra: 1.44 × 10¹⁵ Bq/g
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.
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.
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.
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.
alvin is?
ALVIN!!
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.
I hate the fact I know this
