Band of Stability: Alpha Decay & Nuclear Fission: Videos & Practice Problems

Radioactive isotopes, which are unstable due to an imbalance in neutron and proton numbers, undergo processes like alpha decay and nuclear fission to achieve stability. Alpha decay occurs in isotopes with atomic masses ≥ 210 amu, emitting an alpha particle to reduce nucleons and move towards stability. Nuclear fission involves bombarding an isotope with a neutron, releasing vast energy and splitting the atom into lighter, stable nuclides. This process can trigger a chain reaction, producing more neutrons that perpetuate the reaction. Both mechanisms help isotopes reach a more stable state within the band of stability, with fission also harnessing significant energy release.

Intro to Band of Stability

Understanding the stability of isotopes is crucial in nuclear chemistry. Isotopes that fall outside the band of stability are classified as unstable or radioactive. These isotopes undergo transformations to achieve greater stability by altering their number of neutrons and/or protons. The primary processes through which they achieve this include alpha decay and nuclear fission, but they can also stabilize through beta decay, electron capture, or positron emission.

Alpha decay involves the emission of an alpha particle, which consists of two protons and two neutrons, effectively reducing the atomic number and mass of the original isotope. This process helps the isotope move closer to the band of stability. In contrast, nuclear fission is the splitting of a heavy nucleus into lighter nuclei, releasing a significant amount of energy and neutrons, which can further induce fission in nearby nuclei.

Beta decay occurs when a neutron is transformed into a proton, or vice versa, allowing the isotope to adjust its neutron-to-proton ratio. Electron capture involves an electron being absorbed by a proton, converting it into a neutron, while positron emission involves the release of a positron, which is the antimatter counterpart of an electron, leading to a decrease in the proton count.

When analyzing isotopes, it is essential to consider their position on the neutron-to-proton plot, as this visual representation helps in predicting their stability and the potential decay pathways they may follow to achieve a more stable configuration.

Band of Stability: Alpha Decay

Alpha decay is a process that occurs in certain isotopes, particularly those located in the upper right corner of the neutron-to-proton plot. These isotopes typically possess an excess of both neutrons and protons, making them unstable. For instance, platinum-213, which resides in the red region of this plot, is a prime example of an isotope that undergoes alpha decay.

During alpha decay, platinum-213 emits an alpha particle, resulting in the formation of bismuth-209. This transformation is significant as it reduces the number of neutrons and protons in the nucleus, effectively moving the isotope closer to the band of stability. In the neutron-to-proton plot, the y-axis represents the number of neutrons, while the x-axis represents the number of protons. As platinum-213 decays, it decreases its neutron and proton counts, transitioning from the unstable red area to the more stable green area, which signifies a stable isotope.

This decay process is particularly relevant for isotopes with atomic masses of 210 atomic mass units (AMU) or greater. The overall effect of alpha decay is a reduction in the total number of nucleons (the sum of protons and neutrons), which helps the isotope achieve a more stable configuration. Thus, the movement from the upper right section of the plot into the valley of stability is crucial for the stability of the resulting isotopes.

Band of Stability: Alpha Decay Example

In the context of alpha decay, understanding the transformation of lead-212 (Pb-212) is essential. Lead has an atomic number of 82, indicating it has 82 protons. During alpha decay, an alpha particle, which consists of 2 protons and 2 neutrons, is emitted. This process alters both the mass number and the atomic number of the original nucleus.

For lead-212, the mass number is 212. When an alpha particle is released, the mass number of the resulting daughter nucleus must be calculated by subtracting the mass of the alpha particle (4) from the original mass number:

Mass number of daughter nucleus = 212 - 4 = 208.

Next, we consider the atomic number. The original atomic number is 82, and since the alpha particle contributes 2 protons, the atomic number of the daughter nucleus becomes:

Atomic number of daughter nucleus = 82 - 2 = 80.

Referring to the periodic table, the element with an atomic number of 80 is mercury (Hg). Therefore, the daughter nucleus produced from the alpha decay of lead-212 is mercury-208 (Hg-208). This process illustrates the conservation of mass and charge in nuclear reactions, confirming that the daughter nuclei reside within the band of stability when they fall within the appropriate range of neutron-to-proton ratios.

Band of Stability: Nuclear Fission

Nuclear fission is a process where a neutron is directed at the nucleus of a heavy isotope, such as plutonium-239, resulting in the release of a significant amount of energy. This man-made reaction primarily aims to extract energy by splitting heavy elements, particularly those with atomic mass greater than 209, into lighter daughter nuclides. This splitting reduces the total number of nucleons (protons and neutrons) in the isotope, contributing to energy release.

When a neutron, which has a mass number of 1 and an atomic number of 0, is injected into plutonium-239, it forms an unstable isotope, plutonium-240. This newly formed parent nuclide undergoes fission, breaking apart into two lighter isotopes: zirconium-103 and barium-134. The fission process also releases three additional neutrons and an impressive amount of energy, approximately 207.1 Mega Electron Volts (MeV).

The three neutrons produced can initiate further fission reactions by colliding with other plutonium-239 nuclei, creating a self-sustaining chain reaction. This means that each neutron can trigger additional fission events, leading to the production of more daughter isotopes and even more energy. The daughter products, zirconium-103 and barium-134, fall within the band of stability, indicating that they are more stable than the original heavy isotope.

In summary, nuclear fission not only serves as a powerful energy source through chain reactions but also results in the formation of stable daughter nuclides, enhancing the overall stability of the nuclear reaction products.

Band of Stability: Nuclear Fission Example

Nuclear fission is a significant process, particularly involving uranium-235. When a neutron is injected into uranium-235, it forms uranium-236, which is unstable and subsequently undergoes fission. This reaction produces energy, along with several daughter nuclides and additional neutrons. In this case, we observe one of the daughter products and three neutrons being released.

To identify the missing daughter nuclide, we must ensure that both the total mass number and the total number of protons are conserved in the reaction. Initially, we have a mass number of 236 from uranium-236 on the reactant side. On the product side, we know one daughter nuclide has a mass number of 141, and the three neutrons contribute a total mass of 3 (since each neutron has a mass number of 1). Therefore, the total mass from the known products is:

Mass from daughter nuclide + Mass from neutrons = 141 + 3 = 144.

To maintain the conservation of mass, we need the total mass number on the product side to equal 236. Thus, we can calculate the mass number of the missing daughter nuclide (let's denote it as A) as follows:

A + 144 = 236

A = 236 - 144 = 92.

Next, we analyze the number of protons. The reactant side has 92 protons from uranium-236. The known daughter nuclide contributes 56 protons, and the neutrons do not contribute to the proton count. Therefore, we can find the number of protons in the missing daughter nuclide (denote it as Z) using:

Z + 56 = 92

Z = 92 - 56 = 36.

Referring to the periodic table, the element with an atomic number of 36 is krypton. Therefore, the missing daughter nuclide produced in this fission reaction is krypton-92.

Which of the following is a potential daughter nuclide created from the nuclear fission of uranium-233 that resides near the band of stability? 
a) Strontium-94     
b) Radon-222
c) Curium-247
d) Thorium-232

• A. Strontium-94
• B. Radon-222
• C. Curium-247
• D. Thorium-232

Answer: (A)

Here’s what students ask on this topic:

What is the band of stability in nuclear chemistry?

The band of stability, also known as the valley of stability, is a region on a plot of neutron number (N) versus proton number (Z) where stable isotopes are found. Isotopes within this band have balanced ratios of neutrons to protons, making them stable. Isotopes outside this band are unstable and radioactive, and they undergo various decay processes, such as alpha decay, beta decay, or nuclear fission, to move towards stability. The band of stability helps predict the stability of isotopes and their likely decay pathways.

What is alpha decay and how does it help isotopes achieve stability?

Alpha decay is a type of radioactive decay where an unstable isotope emits an alpha particle, which consists of 2 protons and 2 neutrons (a helium-4 nucleus). This process reduces the number of protons and neutrons in the original isotope, helping it move closer to the band of stability. For example, platinum-213 undergoes alpha decay to form bismuth-209, reducing its nucleon count and achieving a more stable state. Alpha decay typically occurs in heavy isotopes with atomic masses ≥ 210 amu.

How does nuclear fission release energy and contribute to isotope stability?

Nuclear fission involves bombarding a heavy isotope with a neutron, causing it to split into two lighter daughter nuclides and release a significant amount of energy. For instance, when a neutron is injected into plutonium-239, it forms an unstable plutonium-240, which undergoes fission to produce zirconium-103, barium-134, and additional neutrons. This process releases 207.1 MeV of energy and can trigger a chain reaction, where the newly produced neutrons induce further fission events. The resulting daughter nuclides are more stable and fall within the band of stability.

What is a chain reaction in nuclear fission?

A chain reaction in nuclear fission occurs when the neutrons produced from a fission event induce further fission reactions in nearby fissile nuclei. For example, when plutonium-239 undergoes fission, it produces additional neutrons that can react with other plutonium-239 nuclei, perpetuating the process. This continuous series of reactions releases a large amount of energy and produces more stable daughter nuclides. Chain reactions are fundamental to nuclear reactors and atomic bombs, where controlled or uncontrolled fission reactions are harnessed for energy or explosive power.

What are the main differences between alpha decay and nuclear fission?

Alpha decay and nuclear fission are both processes that help unstable isotopes achieve stability, but they differ significantly. Alpha decay involves the emission of an alpha particle (2 protons and 2 neutrons) from a heavy nucleus, reducing its nucleon count and moving it closer to the band of stability. It typically occurs in isotopes with atomic masses ≥ 210 amu. Nuclear fission, on the other hand, involves bombarding a heavy nucleus with a neutron, causing it to split into two lighter daughter nuclides and release a large amount of energy. Fission can trigger a chain reaction, producing more neutrons and perpetuating the process.