Problem 89 - A Complete Resource Book in Chemistry for JEE Main

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 \({ }_{92} \mathrm{U}^{235}\) followed by nuclear fission is (a) 0 (b) 2 (c) 1 (d) 3

Step-by-Step Solution

Answer

The number of neutrons is (d) 3.

Step 1: Understanding Nuclear Fission

Nuclear fission is a process where a heavy nucleus splits into two lighter nuclei, accompanied by a few neutrons and a large amount of energy. In this problem, uranium-235 absorbs a neutron and undergoes fission.

Step 2: Fission Equation

When \(_{92} \mathrm{U}^{235}\) absorbs a neutron, it becomes \(_{92} \mathrm{U}^{236}\). This new nucleus is unstable and splits to form two new nuclei: \(_{54} \mathrm{Xe}^{139}\) and \(_{38} \mathrm{Sr}^{94}\), along with some neutrons.

Step 3: Balancing Atomic Numbers

The atomic number must be conserved in the fission process. The atomic numbers before and after the reaction should balance:\[92 + 0 = 54 + 38 + x\]Here, 'x' refers to the atomic numbers of the neutrons. Thus,\[92 = 92 + x\] \[x = 0\]

Step 4: Balancing Mass Numbers

Similarly, the mass numbers must also balance. Therefore, \[235 + 1 = 139 + 94 + y\]Here, 'y' represents the mass numbers of the emitted neutrons.\[236 = 233 + y\]\[y = 3\]

Step 5: Final Step: Counting Neutrons

The number of neutrons released is equal to 'y', which we calculated as 3. Therefore, three neutrons accompany the nuclear fission process.

Key Concepts

Neutron Emission

Neutron emission is a crucial aspect of nuclear fission. During this process, neutrons are released as a result of a nucleus splitting into smaller parts. When uranium-235 undergoes fission, it absorbs a neutron and becomes unstable, leading to the release of further neutrons. These emitted neutrons can potentially initiate further fission reactions, creating a chain reaction. It's important to note that the number of neutrons emitted can vary, but in our specific case of fission involving uranium-235, three neutrons are typically released. This phenomenon is essential for sustaining a nuclear reaction within reactors or explosions.

Uranium-235 Fission

Uranium-235 fission refers to the process where uranium-235, a heavy isotope, undergoes division into lighter nuclei upon neutron absorption. This radioisotope, with an atomic number of 92, consists of a nucleus that readily splits when bombarded by a slow-moving neutron. After absorbing a neutron, uranium-235 becomes uranium-236, an excited and unstable nucleus. It promptly divides to form smaller, stable nuclei such as xenon-139 and strontium-94. This splitting releases energy and additional neutrons that sustain a continued chain reaction. Uranium-235 is particularly significant due to its ability to undergo fission with thermal (slow) neutrons, making it highly useful in both nuclear reactors and atomic bombs.

Fission Equation

The fission equation describes the transformation of a nucleus during a fission process. For uranium-235, the fission equation can be written as:\[ _{92} \mathrm{U}^{235} + _{0}^{1} \mathrm{n} \rightarrow _{54} \mathrm{Xe}^{139} + _{38} \mathrm{Sr}^{94} + 3_{0}^{1} \mathrm{n} \]In this equation:

• \( _{92} \mathrm{U}^{235} \) is the heavy nucleus initially present.
• \( _{0}^{1} \mathrm{n} \) represents the neutron absorbed by uranium-235.
• \( _{54} \mathrm{Xe}^{139} \) and \( _{38} \mathrm{Sr}^{94} \) are the lighter nuclei formed.
• \( 3_{0}^{1} \mathrm{n} \) signifies the three neutrons emitted as a result.

The equation efficiently represents the conversion of mass and charge, illustrating how total atomic and mass numbers remain balanced post-fission.

Atomic Number Balancing

Atomic number balancing ensures that the sum of atomic numbers (protons count) remains unchanged during a nuclear process. In the fission of uranium-235, the sum of the atomic numbers before and after the reaction must balance to satisfy conservation laws.Initially, uranium-235 has an atomic number of 92. Upon absorbing a neutron, the new system’s atomic numbers are given by:\[ 92 + 0 = 54 + 38 + x \]"\(x\)" represents atomic numbers from neutrons (which are neutral and have an atomic number of 0).Hence:\[ 92 = 54 + 38 + 0 \]Confirming that the atomic numbers before and after fission balance perfectly. Such balance ensures that fission reactions adhere to fundamental nuclear principles, enabling predictable behavior during nuclear processes.