Doesn’t matter. They’re all gonna die,so I see this as an absolute win. (Sorry,I’m old,and have heard the Christmas song enough times this makes me smile)
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)
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.
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.
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.
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?
To expand a bit, you look up the isotope, look at their decay products, and then look up their decay products, and so on until you get to a stable isotope (usually lead or iron).
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 ^235^U 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.
The plutonium gives off some alpha radiation that won’t hurt you if you don’t eat it.
Breathing in particles of plutonium is the danger.
Because it emits alpha particles, plutonium is most dangerous when inhaled. When plutonium particles are inhaled, they lodge in the lung tissue. The alpha particles can kill lung cells, which causes scarring of the lungs, leading to further lung disease and cancer. Plutonium can enter the blood stream from the lungs and travel to the kidneys, meaning that the blood and the kidneys will be exposed to alpha particles. Once plutonium circulates through the body, it concentrates in the bones, liver, and spleen, exposing these organs to alpha particles. Plutonium that is ingested from contaminated food or water does not pose a serious threat to humans because the stomach does not absorb plutonium easily and so it passes out of the body in the feces.
Add comment