Question

How many neutrons are produced from the following fission reaction? $$ { }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{56}^{142} \mathrm{Ba}+{ }_{36}^{91} \mathrm{Kr}+{ }_{0}^{1} \mathrm{n} $$

Short answer

Three neutrons are produced from the fission reaction.

Step-by-step solution

Identify Initial and Final Elements

In the given nuclear fission reaction, you start with one uranium-235 nucleus and one neutron. You end up with barium-142, krypton-91, and an unspecified number of neutrons in addition to the one already shown. The initial and final atomic numbers and mass numbers must match.

Calculate Initial Atomic and Mass Number

The initial total atomic number is 92 (from uranium) + 0 (from the neutron) = 92. The initial mass number is 235 (from uranium) + 1 (from neutron) = 236.

Calculate Final Atomic and Mass Number

The final atomic number is 56 (from barium) + 36 (from krypton) + 0 (from neutron) = 92, which matches the initial atomic number. Similarly, the final mass number is 142 (from barium) + 91 (from krypton) + 1 (from neutron) and the number of additional neutrons \(x\).

Solve for the Missing Neutrons

The final mass number calculated should equal the initial mass number. Thus, 142 (barium) + 91 (krypton) + \(x\cdot 1\) (individual neutrons) = 236. Solving for \(x\), 233 + \(x\) = 236, resulting in \(x=3\).

Confirm Solution Completeness

Check if both atomic and mass numbers match and whether the reaction follows the law of conservation of mass and atomic numbers. Both atomic and mass numbers balance with the addition of 3 neutrons to the already accounted neutron in the equation.

Key concepts

Neutron Calculation

In nuclear fission reactions, accurately calculating the number of neutrons produced is crucial. Neutrons play a critical role in chain reactions, influencing how strongly or weakly a nuclear reaction proceeds. Let's break down the calculation process.

• Start by looking at the equation: \[{ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{56}^{142} \mathrm{Ba}+{ }_{36}^{91} \mathrm{Kr}+{ }_{0}^{1} \mathrm{n} \]
• Recognize the start with one uranium-235 and one neutron, leading to barium, krypton, and some neutrons.
• Your job is to determine the number of these unlisted neutrons.
• Start by considering conservation of mass to solve for these unseen participants in the reaction.

This method ensures you know the specific number of neutrons formed, aiding in understanding the full scope of fission reactions.

Conservation of Mass

Conservation of mass is a fundamental principle in nuclear reactions. It means that the total amount of mass remains constant throughout the reaction. In terms of nuclear physics, this principle applies to both mass and energy due to Einstein's equation \(E = mc^2\). In the context of our fission reaction, this principle is applied as follows:

• The sum of the atomic masses before the reaction equals the sum of atomic masses after the reaction.
• This balance assures that no mass is lost or gained randomly, which is important for energy calculations and practical applications like nuclear power.

The conservation of mass in nuclear fission underscores the precise nature of these reactions.

Atomic Numbers

Atomic numbers help identify elements and ensure the correct number of protons are calculated during reactions. In nuclear fission, the atomic number is crucial as it signifies the identity of elements. For the original exercise:

• Initial atomic number: Sum of uranium and neutron, which is \(92 + 0 = 92\).
• Final atomic number: Sum of barium (56), krypton (36), and neutrons, matching the original 92.
• This validation of atomic numbers demonstrates how nuclear equations keep atom types consistent.

Balancing atomic numbers ensures that proton counts remain correct, maintaining integrity in nuclear transformations.

Uranium Fission

Uranium-235 is a well-known component in nuclear fission reactions. It behaves as a fertile material, meaning it readily undergoes fission when hit with a neutron. Understanding uranium fission involves several key ideas:

• When Uranium-235 absorbs a neutron, it becomes Uranium-236, an unstable isotope.
• This instability causes it to split into smaller atoms (like Barium-142 and Krypton-91), while releasing energy.
• Additional neutrons are produced, enabling the possibility of a chain reaction.

This reaction is significant for its applications in nuclear reactors and weapons, where controlling the fission process leads to controlled energy release.