On Half-Life and radiation part II
There is a lot that I feel needs to be covered still but I really do not want to saddle my poor reader with too much in one sitting, I suspect this will only be the second of many parts on this topic.
In the previous post I did allude to the fact that over time the amount of stuff decreases. What exactly is going on? The law of conservation of matter dictates the amount of stuff remains unchanged.
Well if we look at say Plutonium 238 (that is the energy source for all of the space vehicles out beyond Mars orbit, and a few inside Mars orbit too) what is happening is the nucleus of the Plutonium atoms are breaking apart. Even in a gram of Plutonium there is going to be 2.53×1021 plutonium atoms, that is 2.53 sextillion atoms (yes sextillion is a real number it's a thousand times more than a quintillion of course!).
Well from here it's an application of the law of big numbers, that is plain old statistics, every so often at random an atom will decay. When exactly is random, but the average atom of Plutonium 238 should last about 87.7 years, thus if we have 2.53×1021 atoms and there are 3600 seconds in an hour, 24 hours in a day 365.25 days in a year we get about 2.77 billion seconds (2.77×109) in 87.7 years. So a simple matter of division, 2.53×1021/2.77×109 = 9.13×1011 now this is not correct half the atoms have longer staying power and outlive their half life (the division above presupposed all the atoms decayed within the 87.7 years) But we can see in the order of about half a trillion (5×1011) atoms ought to decay every second, at least for the first while.
Each time a Pu238 decays, it gives off an alpha particle. The alpha bangs around a little, and in so doing gives up heat energy, thus it turns out, every second 1g of Pu238 gives off about 0.5W of thermal (or heat energy). We can capture the heat energy to produce a very modest amount of electricity.
As for the Plutonium, it lost two protons and two neutrons (the makeup of an alpha particle is 2p and 2n), thus if we consider 23894Pu, we subtract two protons and a total of four nucleons, we end up with 23492X, what is this material X? Element number 92 is Uranium, we have some Uranium 234. Is our mass changed?
Well yes actually, a very small amount of mass in the very binding force of the Plutonium atom was converted into kinetic energy that flung the alpha particle off. Remember the famous mass energy equation derived by Albert Einstein? E=mc2? Well the m (mass) was a really tiny number, far less than the weight of an atom but the c2 (c for constant is the speed of light, thus speed of light squared!) is a HUGE number, it is 9 followed by 16 zeros, leaves a fair amount of E (energy) when the dust settles.
For this reason, just a few kilograms of Pu238 make enough heat to keep a spacecraft like Voyager working. Every second almost half a trillion Plutonium atoms per gram of plutonium give up an alpha particle creating heat, the heat drives the bi-metallic thermocouples which produce a small amount (about 300W) of electricity. Of course after 87.7 years half of the Plutonium will have decayed to Uranium and the remaining plutonium will continue to decay with half of what is left decaying over the next 87.7 years.
Eventually pretty much all the plutonium will decay away and the once proud spacecraft will go completely silent drifting at about 62 thousand km/h away from the sun out into the interstellar void.
Of course the Uranium 234 is itself radioactive, with a half life of just under a quarter million years, it also alpha decays 23492U → 23090Th + 42α+2. And this Thorium 230 is also radioactive, a half-life of 75,400 years it alpha decays: 23090Th → 22688Ra + 42α+2. And yes, Ra (or radium) decays, in this yet another alpha decay into Radon 222, which decays into Polonium 218, another alpha decay and we have Lead 214, which is unstable and beta decays into Bismuth 214 which beta decays into Polonium 214, Polonium 214 alpha decays into lead 210 which beta decays into Bismuth 210 which alpha decays into thallium 206 which beta decays into lead 206 and we are finally done. Lead-206 is stable!
What I have described Plutonium to Uranium to Thorium to Radium to Radon to Polonium to Lead to Bismuth to Polonium back to Lead to Bismuth to Thallium to Lead is called a decay chain, and can be represented pictorially, below is a decay chain starting with Plutonium 239 (sorry I cannot find one for Pu238). Although I suspect the Neptunium 237 is a mistake, to get from Np237 to Pu239 you'd need not just a beta decay but also absorption of two neutrons.
The above decay chain (and several others) can be seen here (where this one came from).
Anyway if you're still with me, we covered a lot of material, next time I'll try to explain that diagram better and begin a more detailed discussion of radiation.
In the previous post I did allude to the fact that over time the amount of stuff decreases. What exactly is going on? The law of conservation of matter dictates the amount of stuff remains unchanged.
Well if we look at say Plutonium 238 (that is the energy source for all of the space vehicles out beyond Mars orbit, and a few inside Mars orbit too) what is happening is the nucleus of the Plutonium atoms are breaking apart. Even in a gram of Plutonium there is going to be 2.53×1021 plutonium atoms, that is 2.53 sextillion atoms (yes sextillion is a real number it's a thousand times more than a quintillion of course!).
Well from here it's an application of the law of big numbers, that is plain old statistics, every so often at random an atom will decay. When exactly is random, but the average atom of Plutonium 238 should last about 87.7 years, thus if we have 2.53×1021 atoms and there are 3600 seconds in an hour, 24 hours in a day 365.25 days in a year we get about 2.77 billion seconds (2.77×109) in 87.7 years. So a simple matter of division, 2.53×1021/2.77×109 = 9.13×1011 now this is not correct half the atoms have longer staying power and outlive their half life (the division above presupposed all the atoms decayed within the 87.7 years) But we can see in the order of about half a trillion (5×1011) atoms ought to decay every second, at least for the first while.
Each time a Pu238 decays, it gives off an alpha particle. The alpha bangs around a little, and in so doing gives up heat energy, thus it turns out, every second 1g of Pu238 gives off about 0.5W of thermal (or heat energy). We can capture the heat energy to produce a very modest amount of electricity.
As for the Plutonium, it lost two protons and two neutrons (the makeup of an alpha particle is 2p and 2n), thus if we consider 23894Pu, we subtract two protons and a total of four nucleons, we end up with 23492X, what is this material X? Element number 92 is Uranium, we have some Uranium 234. Is our mass changed?
Well yes actually, a very small amount of mass in the very binding force of the Plutonium atom was converted into kinetic energy that flung the alpha particle off. Remember the famous mass energy equation derived by Albert Einstein? E=mc2? Well the m (mass) was a really tiny number, far less than the weight of an atom but the c2 (c for constant is the speed of light, thus speed of light squared!) is a HUGE number, it is 9 followed by 16 zeros, leaves a fair amount of E (energy) when the dust settles.
For this reason, just a few kilograms of Pu238 make enough heat to keep a spacecraft like Voyager working. Every second almost half a trillion Plutonium atoms per gram of plutonium give up an alpha particle creating heat, the heat drives the bi-metallic thermocouples which produce a small amount (about 300W) of electricity. Of course after 87.7 years half of the Plutonium will have decayed to Uranium and the remaining plutonium will continue to decay with half of what is left decaying over the next 87.7 years.
Eventually pretty much all the plutonium will decay away and the once proud spacecraft will go completely silent drifting at about 62 thousand km/h away from the sun out into the interstellar void.
Of course the Uranium 234 is itself radioactive, with a half life of just under a quarter million years, it also alpha decays 23492U → 23090Th + 42α+2. And this Thorium 230 is also radioactive, a half-life of 75,400 years it alpha decays: 23090Th → 22688Ra + 42α+2. And yes, Ra (or radium) decays, in this yet another alpha decay into Radon 222, which decays into Polonium 218, another alpha decay and we have Lead 214, which is unstable and beta decays into Bismuth 214 which beta decays into Polonium 214, Polonium 214 alpha decays into lead 210 which beta decays into Bismuth 210 which alpha decays into thallium 206 which beta decays into lead 206 and we are finally done. Lead-206 is stable!
What I have described Plutonium to Uranium to Thorium to Radium to Radon to Polonium to Lead to Bismuth to Polonium back to Lead to Bismuth to Thallium to Lead is called a decay chain, and can be represented pictorially, below is a decay chain starting with Plutonium 239 (sorry I cannot find one for Pu238). Although I suspect the Neptunium 237 is a mistake, to get from Np237 to Pu239 you'd need not just a beta decay but also absorption of two neutrons.
The above decay chain (and several others) can be seen here (where this one came from).
Anyway if you're still with me, we covered a lot of material, next time I'll try to explain that diagram better and begin a more detailed discussion of radiation.
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