Band of Stability: Overview - Video Tutorials & Practice Problems

Intepreting the Band of Stability

Now, when it comes to interpreting a neutron to proton plot, remember that the band of stability, the curved portion that's in green represents the area where stable nonradioactive isotopes reside based on their neutron to proton ratios. So if we take a look here, we have in the top right corner where reactions of alpha decay or nuclear fission can take place. We're going to say here, this is common with elements with atomic masses greater than 209 AM U for alpha decay. For example, we have radium 226 it can undergo alpha decay to emit an alpha particle. This will create as a result radon radon 222 as a new isotope nuclear fission, we know that we have a heavy element and it gets shot with a neutron towards its nucleus. This causes a very ins unstable, further unstable radioisotope that breaks down into two daughter radioisotopes as well as three moles of neutrons and a whole lot of energy. In this case here, we will create krypton, krypton as an answer and this will be 89 and 36. Next, we have beta decay. This happens on the left portions, the left side of the valley of stability. This typically happens with those elements that have a great number of neutrons and excess of neutrons beta decay. What is it trying to do? Well, it's trying to decrease the number of neutrons and increase our number of protons. Here, we have carbon 14 undergoing beta decay and it creates as a result of this nitrogen. 14 electron capture happens to the right of our valley of stability or band of stability here. What happens here is we have an excess of protons. So what we need to do is we want to basically increase our number of neutrons and decrease our number of protons. Here, we have cesium 131 undergoing electron capture and positron emission. What we need to take away from this is that although these processes are different, their end result will be the same. They want to again decrease the number of protons, increase the number of neutrons. In the end, they're both gonna make the same type of isotope as a product and that would be xenon 131. So remember we have our neutron or proton plot here on the left, we have our four major sections. We have our red section where alpha decay and nuclear fission typically happen. We have our green portion, which is our valley or band of stability. To the left of that we have where be beta decays typically happen. And then to the right of it where we have electron captures or positron emissions that typically occur.

Band of Stability: Overview Example

In this example question, it says, determine if the following nuclide will undergo alpha decay, beta decay or electron capture and provide the nuclear reaction here, we're dealing with radon 222. Now, upon inspection, we see that its mass number is greater than 209. So remember this typically happens with isotopes that have very high mass numbers. And the answer is alpha decay here. Nuclear fission is also possible, but that's not one of the options. All right. So we're gonna have radon 222 radon has a atomic number of 86. It's undergoing alpha decay. So an alpha particle is emitted as a product here. We need to balance the mass numbers and total number of protons on both sides. We have 222 for our mass number on the reacted side. So we need 222 total on the product side, four of them come from the alpha particle. So we need another 218 218 plus four, gives us 222 we have 86 protons on the reactant side. So we need 86 total on the product side. Two of them already counted for in terms of the alpha particle. So we need another 84. If we look on the periodic table, we see that the element with an atomic number of 84 is polonium po. So this would represent our nuclear reaction where radon 222 undergoes alpha decay. And remember it undergoes alpha decay because its mass number or atomic mass in this case is greater than 2:09 a.m. U. It's incredibly heavy element. And those typically do alpha decay or nuclear fission.

A nuclide of plutonium-241 undergoes 2 alpha decays, 3 beta decays and a gamma emission. What is the product? 

a) Curium                  

b) Neptunium         

c) Uranium                    

d) Thorium

e) Nobelium

• A. Curium
• B. Neptunium
• C. Uranium
• D. Thorium
• E. Nobelium

Band of Stability: Atomic Forces

Now, when it comes to examining a neutron or proton plot, it's also important to take into account atomic forces. Now recall that the nuclear force holds the nucleus together and it's the electrostatic force that wants to pull it apart. Here, we're going to say that our n our neutrons are neutral subatomic particles of an isotope act as a chemical glue that holds together the nucleus. Remember light charges repel one another. If our nucleus was comprised of only protons positively charged subatomic particles, then we repel each other breaking the nucleus apart. The neutrons are kind of acting as in betweens the for those protons, they're not gonna be in direct contact with each other. So it's not gonna be for repulsion. Now, here we're gonna say these forces being out of balance is another reason, radioactive isotopes undergo nuclear decay. We're trying to get to an equilibrium between the two exact forces which gets us closer and more into the band of stability. So remember when we're looking at a typical neutron of proton plot, we say to the left of our band of stability, we have an excess of neutrons where beta decay is more more likely to occur to the right, we have excess protons, which means that electron capture or positron emission can occur. Now, here we're really focusing on those two sections. We're not looking at the top right corner. Since that does alpha decay and nuclear fission things can get a little bit hairy in terms of what can happen. Now, here in the bed of stability, the forces are in balance with one another. So we'd say that they are equal to one another. Now, if we have excess neutrons, excess glue, if we have excess neutrons, what does glue help us to do, helps us to hold things together. So we'd expect our nuclear force to be greater than our electrostatic force overall. And then when we have excess protons, light charges will repel each other. So there's gonna be a greater tendency for repulsion occurring. So if there's more repulsion, there's a greater need to pull the nucleus apart. In these instances, we'd say that nuclear force is less than electrostatic force. So just remember, these atomic forces also play a role in understanding why certain radio isotopes are stable and unstable.

Band of Stability: Overview Example

For this example question, it says which of the following statements is true for the beta decay that would occur with the Cobalt 69 isotope. All right. So Cobalt 69 we're going to say here 69 here is the mass number and the atomic number of Cobalt is 27. Here, we'd have 27 protons and we'd have 69 minus 2742 neutrons. If we come up here and take a look at our plot 27 let's say it's around here or so. And then we just scroll up to around 42 for the number of neutrons which will put us around here. So it looks like that isotope would lie just to the left of our valley of stability. And remember we said in this section, this is where we have an excess number of neutrons and with excess neutrons, excess glue, we'd expect our nuclear force to be greater than our electrostatic force. So if we take a look here, beta decay, what does it do? Beta decay allows us to drop down in terms of the number of neutrons in order to help increase our number of protons decreasing, our amount of glue would help to decrease our nuclear force, increasing our amount of protons would help to increase our electro static force. So here based on that option A would be our answer here. We're trying to get them to be closer in balance with one another to get us within the banner valley of stability. So in this particular example, our answer is option A for B, both of them were decreased. And that's not happening here. Again, our number of neutrons is decreasing as we're moving from the left side towards the Banter Valley of stability. So we'd expect our nuclear force to go down some and yes, there would be a change because we're moving towards the Banner Valley of stability because we're moving from the left side towards it, right. So again, the best answer here is option A.

Determine if the following nuclide will undergo alpha decay, beta decay or positron emission and provide the nuclear reaction: Hydrogen-3       

• A. alpha decay
• B. positron emission
• C. beta decay
• D. positron emission
• E. beta decay

Determine if the following nuclides will undergo alpha decay, beta decay or electron capture and provide the nuclear reaction: Vanadium-50

• A. electron capture
• B. beta decay
• C. alpha decay
• D. electron capture