• ChaoticNeutralCzech@feddit.de
    5·
    1 year ago

    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)

      • ChaoticNeutralCzech@feddit.de
        3·
        1 year ago

        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.

  • Sadrockman@sh.itjust.works
    2·
    1 year ago

    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)

    • hallettj@beehaw.orgEnglish
      1·
      1 year ago

      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.

    • ChaoticNeutralCzech@feddit.de
      2·
      1 year ago

      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.