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

Short answer

3 neutrons are emitted during the controlled nuclear fission of uranium-235.

Step-by-step solution

Understanding Nuclear Fission

Nuclear fission is a reaction in which a heavy nucleus splits into smaller nuclei, with the possible generation of neutrons, and a large amount of energy. This question involves the fission of uranium-235 ({ }_{92}^{235}mathrm{U}) into xenon-142 ({ }_{54}^{142}mathrm{Xe}) and strontium-90 ({ }_{38}^{90}mathrm{Sr}). In addition to these products, neutrons are usually emitted during fission.

Calculating the Number of Neutrons in Reactants and Products

To determine the number of emitted neutrons, we need to know the number of neutrons in the uranium nucleus before the reaction (235 - 92 = 143 neutrons) and the total number of neutrons in the two resulting nuclei (142 - 54 = 88 neutrons for xenon and 90 - 38 = 52 neutrons for strontium).

Determining Neutrons Lost or Gained

The number of neutrons emitted is the difference between the total number of neutrons in the original nucleus and the number of neutrons in the products. If we add up the neutrons in the fission products (88 + 52), we get 140 neutrons. Since we started with 143 neutrons, we subtract the total neutrons in the products from the original neutron count (143 - 140 = 3).

Key concepts

Controlled Nuclear Fission

Nuclear fission is a fundamental process in nuclear physics where a neutron collides with a heavy nucleus, causing it to split into two smaller nuclei. In controlled nuclear fission, this split is managed carefully to harness energy for power generation. The process releases a significant amount of energy due to the conversion of mass into energy as per Einstein's theory of relativity, encapsulated in the equation \(E=mc^2\).

In a nuclear reactor, controlled fission occurs within the reactor core, where uranium-235 ({ }_{92}^{235}U) is the most commonly used fuel. To maintain a sustainable and safe power output, the reaction is kept at a steady rate using control rods that absorb excess neutrons and coolant to remove the heat produced. Uncontrolled fission, on the other hand, can lead to a dangerous release of energy, as seen in nuclear weapons or reactor meltdowns.

Neutron Emission Calculation

Calculating neutron emission is key to understanding nuclear reactions. Neutrons are subatomic particles with no electric charge that play a crucial role in nuclear fission. When uranium-235 undergoes fission, it not only produces smaller nuclei but also releases extra neutrons.

To calculate the number of neutrons emitted, one must account for the imbalance in neutron numbers before and after the reaction. The number of neutrons present in the original uranium nucleus is determined by subtracting the atomic number from its mass number. Following fission, the neutrons are found in the resulting nuclei and as free emitted neutrons. By comparing the initial and final neutron counts, one can ascertain the number of emitted neutrons. This calculation is fundamental as the emitted neutrons can go on to initiate further fission reactions, which is the principle behind a nuclear chain reaction.

Nuclear Reaction Equations

Nuclear reaction equations are written to represent the changes occurring during a nuclear reaction. They must balance both mass and charge across the reactants and products. In the case of uranium-235 fission, the equation summarizing the nuclear reaction includes the initial uranium nucleus, the two resulting nuclei, xenon-142 and strontium-90, and the free neutrons.

The balanced equation illustrates the law of conservation of nucleons, ensuring that the total count of protons and neutrons remains constant. The equation is vital for understanding the products' identity, the energy released, and for predicting the behavior of a nuclear reaction. A properly balanced nuclear equation serves as the blueprint for calculating the practical aspects of nuclear reactions, such as neutron emission and energy output.