THMG292 – Radioactive half lives, fission and fusion

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I think one of the first things that has to be understood before we talk about radioactive decay is what can decay. Basically anything with more than 84 protons is unstable and will tend to decay. You can have isotopes with fewer protons decay, but its uncommon. The property that dictates how radioactive something is is the ratio neutron / proton ratio. If the isotope is found to be neutron rich, then its unstable. On the other hand if its neutron “light?” then it can also be unstable. 

We can have decay in a few manners that we may or may not be familiar with. We can have Alpha particles poppin off, or maybe some beta emission, or even gamma radiation. Further we could have a few types that are way less common like positron emission or electron capture. 

In the case of an alpha particle discharge, we shoot off 2 protons and 2 neutrons. That s a 4 mass swing! 

If we have a beta emission we shoot an electron from the nucleus. “WAIT A SECOND BOB, ELECTRONS AREN’T IN THE NEUCLUS!?” Hold your horses. 

We’ve done a deep dive on this topic, but in order to keep all of this in the same show, I’ll go over it quickly. Lets says we had a I-131 atom and it gives off a beta particle (an electron). So our I-131 remains with a mass of 131. The atomic number is 54 (which is 53 – (-1)) If we look at this purely at the atomic number of 54 it “identifies as Xenon. But the mass number doesn’t change going from I-131 to Xe-131, but the atomic number went down one. In the iodine neucleus a neutron was converted into an electron and shot out, what was left is a proton. Whew…ok, back to the regularly scheduled content.

If you could sit and watch a single atom of radioactive isotopes let’s say uranium 238. The problem would be that you couldn’t predict when that particular atom would decay. It might happen now later next week next Millennium there’s really no way to understand.

So now let’s say we have a big sample something big enough that we would be in where mathematicians call a statistically significant sample size, at this point we may be able to point out a pattern. Now we all understand that it takes time for atoms to decay and go away. So then you can also say that the same amount of time for half of the amount of atoms to decay which means that we also have half the amount still there can be calculated. So we call this time that it takes 1/2 of them to go away the half life of an isotope, or the t1/2

if we had to calculate out the half life decay of a radioactive isotope the problem would be it’s not a simple math equation. Meaning it’s not linear. So for example you couldn’t find the remaining amount of isotope if let’s say it’s 4.7 half lives by looking between 4 and 5 half lives. So if we wanted to find the amount or the times with a simple multiplication of a half life we would use this equation.

T1/2 = 0.6963/k

Then

Ln (Nt/No) = -kt


Now, maybe you’re not a math nerd, then you’re gonna note that there’s a little something different here this is what they would call an natural logarithm. There’s also another one called AB’s ilaug and that is not the base 10 log but it’s on your calculator so don’t worry about it. In here the end to the oh is the amount of radioactive isotope that we start with in terms of grams or maybe even a percentage. The end to the T is the amount of radioactive isotope that’s left at some time and the t1/2 is the half-life. Obviously, this whole formula can be switched around to find for whatever you want.

Radioactive dating

As far as hazmat response utilizing half lives in the fields is not realistic, however understanding how it all works is helpful. One of the things you might see on TV is the use radioactive half lives to carbon date. The specific isotope they’re talking about is carbon 14 which is a specific radioactive isotope of carbon and it’s produced in the upper atmosphere by cosmic radiation. The vast majority of carbon found in the atmosphere is in the form of carbon dioxide but a but very little of it contains carbon 14. And as we know plants drink in carbon dioxide and some of that would be having carbon 14 in it. So this carbon 14 is part of the chemical cellular properties of the plant. Then the plants are eaten by animals making carbon 14 a part of the cellular structure of all living things. It’s the circle of life man

So as long as you’re alive the amount of C-14 in you remains constant, but when you die the amount of C-14 begins to decrease. Now this number of the half life of C-14 is known. If you curious it’s 5730 years. So based on this they can figure out how long ago you died. 

one of the common misconceptions of carbon dating is that you need to be alive in order for it to work so something like a meteorite or a rock from the space would not work because it was nonliving. That doesn’t mean that scientists are out of luck they just use a different isotope such as potassium 40

Breaking Elements Apart with Nuclear Fission

Now we jump in all wayback machines and land in the 1930s, scientists began to discover that some of these nuclear reactions could be initiated and controlled easily. What they would do is they would take a large isotope and break it in to smaller parts by shooting neutrons at it. Now this wasn’t something they can do in the garage they needed incredibly big accelerators in order to shoot these neutrons at the speed that would work. But the point is the collision caused the larger isotope to break apart in a process known as nuclear fission.

The following equationshows the nuclear fission of uranium-235:


Mass defect: Where does all that energy come from?

We talked about nuclear fission we think about nuclear bombs. Something in a very small package that releases a ridiculous amount of energy. So the question comes where does all that energy come from?

So let’s say we were able to smash a neutron into a large isotope and we cook extremely accurate measurements of all the masses of the atoms and even the sub-atomic particles starting with the beginning and ending with the end and we would find that there is some things that are missing.

Wait a second Bob I’ve been told since I was a little kid that matter is neither created or destroyed. Well in this case the loss of matter is called a mass defect what happens is the missing matter is converted into energy.


You can actually calculate the amount of energy that’s produced during a nuclear explosion or a reaction with a fairly simple equation that I developed while jotting some notes down on a bar napkin. You may have heard of this. It’s something I like to call E equals MC squared.

In this equation E is the amount of energy produced, minus the missing mass or the mass defect. C is the speed of light in a vacuum which is an incredibly large number at that. So you can see even when multiplied by a small amount of mass it yields an extremely large amount of energy.


Chain reactions and critical mass

Formula for the fission of U-235

Now breaking one isotope into a smaller set is cool if you could do it once. But how do you do it over and over and over. Something we call a chain reaction. So if we look at this formula forward unit uranium 235, we can see that one neutron was used to start it but 3 neutrons are produced at the other side. So if these 3 neutrons encounter other uranium 235 atoms, they could initiate other fissions producing even more neutrons. This is how a nuclear bomb goes off with a constant chemical chain reaction

so if we would able to initiate a chain reaction that had more neutrons than needed to actually smash things apart then we’d be successful in continuing the chain reaction.

Here’s a small problem with uranium 235, it’s not that common to find. If we use the more common isotope of uranium called uranium 238 and we wrote that equation now, we would see that we would get one neutron in and one neutron out. So you can imagine it’s a little bit more difficult to do in your garage and you would initially imagine.

So, when you have an excess of neutrons at the end of the equation it’s more apt to support chain reactions and we would call this type of isotope a fissionable isotope. Currently there are two main types of isotopes that are what we would call fissionable and that would be uranium 235 and plutonium 239.

Another term you may hear in the nuclear field is the term critical mass. This is the amount of mass that at a minimum must be achieved in order for you to support a self sustaining chain reaction. And it’s all based upon the amount of neutrons. Even the small sample then is little likelihood of it being able to shoot out a neutron and hit another unit uranium 235 nucleus. So no nucleus hit no extra electrons and no energy is released, the reaction just basically stops. Show if you want the reaction to keep going you must achieve at least a critical mass. Anything less than this is called subcritical.

Coming Together with Nuclear Fusion

So let’s flip the coin. Let’s talk about another process that this scientists have figured out called fusion. fusion is basically the opposite of fission. So in vision we take a heavy nucleus and split the small nucleus or nuclei. With fusion we take lighter smaller nuclei and fuse them together into a bigger heavier nucleus.

You may have heard this on TV’s cold fusion which is something that they’re working on, but it’s the reaction that drives the sun. On the sun it’s a series of nuclear reactions that puts four hydrogen isotopes are fused into a helium isotope. Obviously this release releases a tremendous amount of energy. Here on earth we can’t do that, we use two other types of isotope like deuterium which is H2 and treat him with each three. Deuterium is a minor isotope of hydrogen but it’s still pretty abundant, but tritium is really hard and we have to make it, by smashing deuterium


The following equation shows the fusion reaction:

H+H → He + on

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