Band of Stability: Overview: Videos & Practice Problems

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

Understanding the neutron to proton plot is essential for interpreting the stability of isotopes. The band of stability, represented by a green curved area, indicates where stable, non-radioactive isotopes are found based on their neutron to proton ratios. Isotopes that fall outside this band are typically unstable and undergo various types of radioactive decay.

In the upper right corner of the plot, reactions such as alpha decay and nuclear fission are common, particularly for elements with atomic masses greater than 209 AMU. For instance, radium-226 can undergo alpha decay, emitting an alpha particle and transforming into radon-222. In nuclear fission, a heavy element is bombarded with a neutron, resulting in an unstable isotope that splits into two daughter isotopes, releasing three neutrons and a significant amount of energy. An example of this process is the fission of uranium, which can produce krypton-89 (with atomic number 36).

On the left side of the band of stability, beta decay occurs, typically in isotopes with an excess of neutrons. This process aims to reduce the number of neutrons while increasing the number of protons. For example, carbon-14 undergoes beta decay to form nitrogen-14.

To the right of the band of stability, electron capture and positron emission take place, often in isotopes with an excess of protons. These processes work to increase the number of neutrons and decrease the number of protons. An example is cesium-131, which can undergo electron capture to produce xenon-131.

Despite the differences in these decay processes, they share a common goal: to achieve a more stable neutron to proton ratio. The neutron to proton plot is divided into four major sections: the red area where alpha decay and nuclear fission occur, the green band of stability, the left side where beta decay happens, and the right side where electron captures and positron emissions take place. Understanding these sections helps in predicting the behavior of isotopes and their pathways to stability.

Band of Stability: Identify Nuclear Reaction Example

To determine the type of decay for radon-222, we first note its mass number, which is 222. Elements with mass numbers greater than 209 often undergo alpha decay due to their instability. In this case, radon-222, with an atomic number of 86, emits an alpha particle during the decay process.

In alpha decay, the nucleus releases an alpha particle, which consists of 2 protons and 2 neutrons, effectively reducing the mass number by 4 and the atomic number by 2. To balance the nuclear reaction, we start with the reactants:

Radon-222: ₈₆Rn²²²

When it undergoes alpha decay, the reaction can be represented as follows:

₈₆Rn²²² → ₈₄Po²¹⁸ + ₂He⁴

Here, the mass number on the product side is balanced as follows: 222 (from radon) equals 218 (from polonium) plus 4 (from the alpha particle). The atomic number is also balanced: 86 (from radon) equals 84 (from polonium) plus 2 (from the alpha particle).

Thus, the nuclear reaction for radon-222 undergoing alpha decay results in polonium-218 and an emitted alpha particle. This decay process is characteristic of heavy elements, which tend to become more stable by emitting alpha particles.

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

Answer: (B)

Band of Stability: Atomic Forces

When analyzing a neutron to proton plot, it is crucial to consider the interplay of atomic forces that influence nuclear stability. The nuclear force, which is responsible for holding the nucleus together, contrasts with the electrostatic force that tends to separate it. Neutrons, being neutral subatomic particles, act as a form of chemical glue within the nucleus, mitigating the repulsive forces between positively charged protons. If a nucleus consisted solely of protons, the repulsion would lead to instability and disintegration.

The balance of these forces is essential for the stability of isotopes. An imbalance can result in radioactive decay as isotopes strive to reach equilibrium between the nuclear and electrostatic forces. In a typical neutron to proton plot, the band of stability represents this equilibrium. To the left of this band, there is an excess of neutrons, which increases the likelihood of beta decay. Conversely, to the right, an excess of protons can lead to processes such as electron capture or positron emission.

Within the band of stability, the nuclear force and electrostatic force are balanced. When there are excess neutrons, the nuclear force predominates, effectively holding the nucleus together. In contrast, an excess of protons results in increased repulsion, indicating that the electrostatic force is stronger, which can destabilize the nucleus. Understanding these atomic forces is vital for comprehending the stability and instability of various radioisotopes.

Band of Stability: Overview Example

In the context of beta decay for the Cobalt-69 isotope, it is essential to understand the composition of the isotope. Cobalt-69 has a mass number of 69 and an atomic number of 27, indicating it contains 27 protons and 42 neutrons (calculated as 69 - 27). When visualizing the stability of isotopes, Cobalt-69 lies just to the left of the valley of stability, which signifies an excess of neutrons.

The valley of stability represents a balance between the nuclear force and the electrostatic force. In isotopes with an excess of neutrons, the nuclear force, which is responsible for holding the nucleus together, is greater than the electrostatic force that repels protons from each other. During beta decay, a neutron is transformed into a proton, which decreases the number of neutrons and increases the number of protons. This process helps to move the isotope closer to the valley of stability.

As a result of beta decay, the nuclear force decreases due to the reduction in the number of neutrons, while the electrostatic force increases with the addition of protons. This shift is crucial for achieving a more stable configuration. Therefore, the correct statement regarding the beta decay of Cobalt-69 is that it facilitates a transition towards a more balanced state, ultimately moving the isotope closer to the valley of stability.

In summary, the beta decay of Cobalt-69 results in a decrease in the number of neutrons and an increase in the number of protons, aligning with the goal of achieving stability within the nuclear structure.

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

Answer: (C)

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

Answer: (A)

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.