Problem 11 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The number of neutrons emitted when \({ }_{92}^{235} \mathrm{U}\) undergoes controlled nuclear fission to \({ }_{54}^{142} \mathrm{Xe}\) and \({ }_{38}^{90} \mathrm{Sr}\) is

Step-by-Step Solution

Answer

3 neutrons are emitted.

Step 1: Understanding the Nuclear Reaction

In a controlled nuclear fission reaction, a heavy nucleus splits into two lighter nuclei and some neutrons are released. First, identify the given nuclei in the reaction: the uranium-235 nucleus and the resulting xenon-142 and strontium-90 nuclei.

Step 2: Writing the Fission Equation

The reaction can be written as: \[{}_{92}^{235} ext{U} ightarrow {}_{54}^{142} ext{Xe} + {}_{38}^{90} ext{Sr} + x ext{ }n\], where \(x\) represents the number of emitted neutrons.

Step 3: Conservation of Atomic Number

Apply the conservation of atomic number (protons): The total atomic number before the reaction must equal the total after. So, \(92 = 54 + 38\), confirming no errors regarding atomic numbers.

Step 4: Conservation of Mass Number

Apply the conservation of mass number (neutrons plus protons): The sum of mass numbers of the resulting nuclei and neutrons must equal the original mass number. Calculate this: \(235 = 142 + 90 + x\).

Step 5: Solving for Unknown Neutrons

Set up the equation from the previous step: \(235 = 142 + 90 + x\). Solve for \(x\): \(235 = 232 + x\), giving \(x = 3\).

Key Concepts

Neutrons

Neutrons play a pivotal role in nuclear fission, acting as the particles that can initiate a chain reaction and are products of the fission process. In a nuclear fission reaction, when a large atomic nucleus such as uranium-235 absorbs an additional neutron, it becomes unstable and splits into smaller nuclei. This splitting releases energy and emits more neutrons.

• These free neutrons can then collide with other uranium-235 nuclei, potentially causing further fission reactions.
• This process is what makes nuclear reactors so powerful as they convert the stored nuclear energy into usable energy.

Understanding the number of emitted neutrons is crucial because it influences the reaction's sustainability and control. In the given exercise, when uranium-235 undergoes fission, three neutrons are emitted, which participate in further reactions, continuing the chain reaction.

Uranium-235

Uranium-235 is a significant isotope in nuclear fission due to its ability to easily undergo fission upon absorbing a neutron. It is one of the most common isotopes used in nuclear reactors and atomic bombs.

• Uranium-235 has 92 protons and 143 neutrons, leading to a combined mass number of 235.
• This isotope is key in sustaining a chain reaction due to its properties to emit additional neutrons upon fission.

When uranium-235 undergoes fission, it splits into smaller nuclei, such as xenon-142 and strontium-90, while releasing energy and free neutrons. This property makes it very valuable in nuclear power generation, where the goal is to harness the energy released from these reactions.

Mass Number Conservation

In nuclear reactions such as fission, the law of conservation of mass number is a fundamental principle. This means that the sum of the mass numbers of the reactants equals the sum of the mass numbers of the products and any emitted neutrons.For the given reaction involving uranium-235, this principle can be observed:

• The initial mass number of uranium-235 is 235.
• After fission, the sum of the mass numbers of xenon-142, strontium-90, and the emitted neutrons must also be 235.

The equation used to solve for the number of neutrons included these components:\[235 = 142 + 90 + x\]Where \(x\) represents the number of neutrons emitted. Solving yields 3 neutrons, ensuring mass number conservation.

Atomic Number Conservation

Atomic number conservation is another critical aspect of nuclear fission. It involves maintaining the total number of protons, crucial for understanding how nuclear equations balance. In the exercise, the uranium-235 atom, with an atomic number of 92, splits into xenon-142 and strontium-90:

• Xenon's atomic number is 54.
• Strontium's atomic number is 38.

Adding these together gives 54 + 38 = 92, which matches the atomic number of the original uranium-235 nucleus. This conservation ensures that the fundamental structure at the nuclear level is maintained, providing a balanced perspective of how nuclear reactions preserve certain properties, despite significant changes occurring at the atomic nucleus level.