Band of Stability: Overview - Online Tutor, Practice Problems & Exam Prep

Understanding the stability of isotopes involves interpreting their neutron-to-proton ratios, depicted on a neutron-proton plot. Stable isotopes reside within the band of stability. Isotopes outside this band undergo radioactive decay to reach stability: alpha decay and nuclear fission occur in heavy elements (e.g., radium-226 to radon-222), while beta decay is seen in neutron-rich isotopes (e.g., carbon-14 to nitrogen-14). Isotopes with excess protons may undergo electron capture or positron emission (e.g., cesium-131 to xenon-131). The balance of nuclear forces, which hold the nucleus together, and electrostatic forces, which tend to pull it apart, also influences isotopic stability. Neutrons act as a 'chemical glue,' mitigating repulsion between protons and contributing to the stability of the nucleus. Understanding these forces and decay processes is crucial for grasping why certain isotopes are stable or radioactive.

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 non-radioactive 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 AMU.

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 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 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, 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, an 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 nitrogen 14.

Electron capture happens to the right of our valley of stability or band of stability. 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 going to 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 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 it's 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 going to 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 reactant side, so we need 222 total on the product side. Four of them come from the alpha particle, so we need another two. 18218 + 4 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 O. 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 209 AMU. It's incredibly heavy element and those typically do alpha decay or nuclear fission.

Rn 222 → Po 218 + α 4

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 a nucleus together, and it's the electrostatic force that wants to pull it apart. Here we're going to say that our neutrons are neutral. Subatomic particles of an isotope act as a chemical glue that holds together the nucleus.

Remember, like 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 for those protons. They're not going to be in direct contact with each other, so they're not going to be for repulsion. Now here we're going to 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 neutral proton plot, we say to the left of our band of stability we have an excess of neutrons or beta decay is more likely to occur. To the right, we have excess protons, which means that electron capture 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 band 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 repel each other. So there's going to 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<electrostatic force. So just remember, these atomic forces also play a role in understanding why certain radioisotopes 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 - 27 = 42 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.

O 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 electrostatic force. So here based on that option A would be our answer.

Here we're trying to get them to be closer and balanced with one another to get us within the batter 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 banner value 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 matter 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

Here’s what students ask on this topic:

What is the band of stability?

The band of stability, also known as the belt of stability, refers to the region on a graph of neutron number (_N) versus proton number (_Z) where stable isotopes reside. This band illustrates which combinations of protons and neutrons result in stable nuclei that do not undergo radioactive decay. Atoms within this band have a balanced ratio of neutrons to protons that allows the strong nuclear force to effectively counteract the repulsive forces between protons, thus ensuring stability.

For lighter elements (up to iron), the ratio of neutrons to protons in stable nuclei is approximately 1:1. As atoms get heavier, they require a higher neutron-to-proton ratio to remain stable, because additional neutrons help to mitigate the increasing repulsive forces between the greater number of protons. Outside the band of stability, nuclei are unstable and are more likely to undergo radioactive decay in an attempt to reach a stable state. This concept is critical in nuclear physics and helps to explain why certain isotopes are radioactive while others are not.

Do the following nuclei, which do not lie in the band of stability, decay in a certain way?

Nuclei that do not lie within the band of stability typically decay to reach a more stable state. There are several ways in which they can decay:

1. Alpha Decay: Heavy nuclei with atomic numbers greater than 82 may undergo alpha decay, where they emit an alpha particle (two protons and two neutrons) to achieve a more stable nucleus.
2. Beta Decay: There are two types of beta decay:
   • Beta Minus (β^-) Decay: Neutron-rich nuclei can transform a neutron into a proton while emitting an electron (beta particle) and an antineutrino.
   • Beta Plus (β⁺) Decay or Positron Emission: Proton-rich nuclei can convert a proton into a neutron, emitting a positron (the electron's antiparticle) and a neutrino.
3. Electron Capture: Another process for proton-rich nuclei is electron capture, where an inner orbital electron is captured by the nucleus, transforming a proton into a neutron and emitting a neutrino.
4. Gamma Decay: After alpha or beta decay, the daughter nucleus may still be in an excited state. It can release excess energy in the form of gamma radiation to reach a lower energy state.
5. Spontaneous Fission: Very heavy nuclei might split into two or more smaller nuclei and some free neutrons.

What types of radioactive decay will occur below the band of stability (close to protons/x axis)?

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Below the band of stability on the chart of nuclides, you'll find that nuclei have a proton to neutron ratio that is too high. This means they have too many protons to be stable. To move back towards stability, these nuclei will undergo types of radioactive decay that convert protons into neutrons or otherwise reduce the number of protons.

The main types of decay processes that occur in this region are:

1. Beta-plus decay (β<sup>+</sup> decay): In this process, a proton is transformed into a neutron, a positron (which is the antimatter counterpart of an electron), and a neutrino. The positron is emitted from the nucleus, and the neutrino carries away some energy.
2. Electron capture: Instead of emitting a positron, the nucleus captures an orbiting electron which combines with a proton to form a neutron and a neutrino. The neutrino is then emitted from the nucleus.

Both of these decay processes increase the neutron to proton ratio, helping the nucleus move back towards the band of stability.

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How does the slope of the band of stability change as the number of protons increases?

The band of stability on a graph of neutron number versus proton number (N vs. Z) represents the stable isotopes of elements. As the number of protons increases, the slope of the band of stability gradually decreases. This means that heavier nuclei require a greater number of neutrons compared to protons to remain stable.

In lighter elements (up to about Z₂₀), the ratio of neutrons to protons (N/Z) for stable isotopes is approximately 1:1. However, as the elements get heavier, this ratio increases due to the growing repulsive force between the positively charged protons in the nucleus. To counterbalance this repulsion and stabilize the nucleus, more neutrons are needed. This results in the slope of the band of stability trending downwards, indicating that stable isotopes of heavier elements have increasingly larger numbers of neutrons relative to protons.