Question

The number of neutrons accompanying the formation of \({ }_{54} \mathrm{Xe}^{139}\) and \({ }_{38} \mathrm{Sr}^{94}\) from the absorption of slow neutron by \({ }_{92} \mathrm{U}^{235}\) by nuclear fission is (a) 0 (b) 2 (c) 1 (d) 3

Short answer

The number of neutrons released during the formation of Xenon-139 and Strontium-94 from Uranium-235 by nuclear fission is 3 (d).

Step-by-step solution

Identify the Original Nucleus

Start by identifying the original heavy nucleus that undergoes fission: Uranium-235 (_ {92}^{235}U). This is the nucleus that absorbs a slow neutron and subsequently splits.

Identify the Fission Products

Identify the two fission products given in the exercise: Xenon-139 (_ {54}^{139}Xe) and Strontium-94 (_{38}^{94}Sr).

Determine the Change in Nucleon Number

Calculate the change in nucleon number during fission. The original Uranium-235 will absorb a neutron (which has a nucleon number of 1), thus the total nucleons involved before the fission is 235 (from Uranium) + 1 (from the absorbed neutron) = 236.

Calculate the Total Nucleon Number of the Fission Products

Add the nucleon numbers of the two fission products: 139 (from Xenon-139) + 94 (from Strontium-94) = 233.

Calculate the Number of Neutrons Released

Subtract the total nucleon number of the fission products from the total nucleons present before the fission to find the number of neutrons released. 236 (from original nucleons) - 233 (from the fission products) = 3 neutrons released.

Key concepts

Nuclear Chemistry

Nuclear chemistry is the study of the chemical and physical properties of elements as influenced by changes in the structure of the atomic nucleus. When we talk about nuclear fission, which is a key topic in nuclear chemistry, we refer to the process by which a heavy nucleus, such as uranium-235, splits into two smaller nuclei when hit by a neutron. This splitting releases vast amounts of energy and additional neutrons, which can then go on to initiate further fission reactions—this is known as a chain reaction. Understanding nuclear fission is not just about comprehending a singular reaction; it's about appreciating a set of reactions that have significant implications in fields like nuclear power generation and nuclear weapons development.

Let's consider the detailed process: When uranium-235 absorbs a slow-moving neutron, it becomes uranium-236—an unstable nuclide that rapidly splits into fission products such as xenon-139 and strontium-94, as well as additional neutrons. These neutrons can be calculated, as shown in our exercise, to determine the byproducts and efficiency of the fission process. The calculation process involves understanding the conservation of nucleons (protons and neutrons) and the resulting mass-energy equivalence implied by E=mc², the most famous equation attributed to Albert Einstein.

Neutron Calculation

Neutron calculation is a critical aspect when solving nuclear fission problems. Since the number of neutrons before and after a fission event must be conserved, their calculation encapsulates both the balance of nuclear masses and the maintenance of nuclear stability. The step-by-step solution provided for our textbook exercise illustrates this neatly. You begin by counting the number of nucleons, which include protons and neutrons, in the initial nucleus after the neutron absorption. Then, you count the number of nucleons in the fission products. The difference gives you the number of neutrons released.

In our exercise, after uranium-235 absorbs a neutron, it becomes uranium-236; breaking down into xenon-139 and strontium-94 leaves us with a discrepancy of 3 nucleons. These 3 nucleons are the additional neutrons released during the fission process. Managing such calculations is fundamental for anyone studying nuclear physics or engineering because it allows the prediction of the outcome of the fission process and the understanding of neutron economy in a reactor core, where maintaining a stable chain reaction is crucial.

Fission Products

Fission products are the resulting nuclei after the fission of a heavy nucleus such as uranium-235. Each fission event typically results in two fission products along with the release of several neutrons and a considerable amount of energy. In our exercise, the fission products are xenon-139 and strontium-94. These products are critical to understand for multiple reasons: they're radioactive, they contribute to the chain reaction, and they need to be managed carefully in terms of waste disposal. Furthermore, their specific radioactivities and half-lives play a role in determining the radiation hazards and cooling requirements post the shutdown of a nuclear reactor.

These byproducts vary in their atomic mass and can range from lighter to near equal mass compared to the original nucleus. It's important for students to realize that the characteristics of these fission products—such as their stability, their capability to absorb further neutrons, and the type and intensity of the radiation they emit—are significant when considering the overall safety and efficiency of nuclear power plants. The formation of these products and the subsequent release of neutrons, as outlined in our neutron calculation, confirm the continuity of nuclear chain reactions in controlled environments like reactors or uncontrolled environments like atomic detonations.