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Plutonium isotope ${ }^{239}$ Pu decays by alpha decay with a halflife of $24100 mathrm{y}$. How many milligrams of helium are produced by an initially pure $12.0 m...

Question

Plutonium isotope ${ }^{239}$ Pu decays by alpha decay with a halflife of $24100 mathrm{y}$. How many milligrams of helium are produced by an initially pure $12.0 mathrm{~g}$ sample of ${ }^{239} mathrm{Pu}$ at the end of $20000 mathrm{y}$ ? (Consider only the helium produced directly by the plutonium and not by any by-products of the decay process.)

Plutonium isotope ${ }^{239}$ Pu decays by alpha decay with a halflife of $24100 mathrm{y}$. How many milligrams of helium are produced by an initially pure $12.0 mathrm{~g}$ sample of ${ }^{239} mathrm{Pu}$ at the end of $20000 mathrm{y}$ ? (Consider only the helium produced directly by the plutonium and not by any by-products of the decay process.)



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Plutonium isotope ${ }^{239}$ Pu decays by alpha decay with a halflife of $24100 \mathrm{y}$. How many milligrams of helium are produced by an initially pure $12.0 \mathrm{~g}$ sample of ${ }^{239} \mathrm{Pu}$ at the end of $20000 \mathrm{y}$ ? (Consider only the helium produced directly by the plutonium and not by any by-products of the decay process.)

So were asked what nuclear is produced from the falling radioactive case. So the first case, we're considering his Alfa decay of plutonium to 39. So remembering that Alfred K. A Helium Atom Limited, which has talking massive four opens two protons, you know that the next caper must have two fewer protons in a mass, and both of these products must add up to the mass of our initial sample. So this tells us looking at her periodic table, but it must be left with uranium 2 35 because it's not my number of 92. We're on second case for big bouquet of sodium. You know, the electron is admitted, which has zero mass, but also because the electron admitted no a neutron has a kid in tow, a proton leaving on that atomic number of 12 11. So again, with a period table, you see, this is magnesium. 12 has a massive 24. So lastly, big plastic a minute remaining closet throne, which has no mass now, while the protons has essentially accepted an electron and is now has the same mass but is now a neutron star atomic number are next to keep our miss have one fewer four times compared to oxygen again with people. This leaves nitrogen seven rather next 15 has an atomic number of saying, and those are two key products.

42.28. We, uh, want to think about the isotope plutonium to 39 has produced is a byproduct of nuclear reactors, and so is a bit of a waste problem. Its half life, we're told, is 2.41 times 10 to the fourth years just quite a while. First, we want to find out how many nuclei we have in a chemically lethal dose of two milligrams, in addition to being that dangerous because it's radioactive. Plutonium is also, by itself fairly toxic, just chemically. So it's stuff that you would much prefer to avoid, given any kind of choice in the matter. Then we want to know what the decay rate of this amount of plutonium it's So for a the number of plutonium atoms we would have, it's gonna be the total mass provided by the solar mass of it. She's always approximately just the same as the mass member of Of the Ice Ato And multiply this by avocados constant to convert for moles, toe number of things, and we find that this is 5.4 times tend to the 18th nuclei. So now taking Equation 42 just 20 and rearranging it. Uh, we have that. The re is number of nuclei and the natural log too, provided by the half life. So this is one point for habits tend to the 14th for a year or, uh, 4.60 times 10 for the sixth Becker Els, which is the S I unit rate of decay and his equal toe one over seconds 12 k per second. So you have about four and 1/2 1,000,000 decays per second and two milligrams of plutonium to 39.

42.36. Plutonium to 39 decays by Alfa Decay on the half pipe is strong. Here it's 24,100 years. And so if we start with the initial sample of 12 grams of pure plutonium to 39 how many milligrams of helium is produced from the plutonium decays after 20,000 years? We only want to consider the helium that's produced directly from the plutonium Sze decaying and not from any daughter products of of the plutonium that might cave further or anything like that. So every time a plutonium nucleus decays, we get one alpha particle er, helium nucleus. And so, in order to find the number that decay, it's going to be the initial number minus the number left over after our 20,000 years. Okay, so this is going to be one minus meat to the negative T log two divided by 1/2 life. But this is off. God response. Tin times, uh, 12 grams provided by 239 grams per mole. Times are exponential thing. We don't need to write again, so this means we're going to get 1.32 times 10 to the 22 health of particles because this is the number of the case that will have occurred from the plutonium. So the mass of the helium is just going to be the mass of a helium atom times the number of helium atoms. So we have the number here particles. It's going to be divided by God, rose number, and then the Moler. Massive helium is four grams per home look and so in milligrams, like a nest for this is 87 0.9 milligrams.

Uranium to 38 to case through Alfa Decay, with 1/2 life of 4.46 times 10 to the nine years. How long would it take for 7/8 of a sample of uranium to 38 to decay? Remember that half life is the time it takes for half a radioactive material to disintegrate by radioactive decay processes. So this means that if you initially start off with a certain quantity after 1/2 life, you'll have half assed much. After a second half, Life will have 1/4 after 1/3 you'll have 18 and so on. So if 7/8 of a sample has decayed, that means that an eighth remains. So that's one to 3/2 lives. If we have 3/2 lives and we know that 1/2 life is 4.46 times tend to the nine years you just multiply the two to get 1.34 times 10 to the 10 years no


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