Question

Write an equation for the fission of \(^{235} \mathrm{U}\) by bombardment with neutrons.

Short answer

The short answer for the fission of \(^{235}\mathrm{U}\) by bombardment with neutrons is: \(^{235}\mathrm{U} + ^1\mathrm{n} \rightarrow ^{144}\mathrm{Ba} + ^{90}\mathrm{Kr} + 3\,^1\mathrm{n}\)

Step-by-step solution

Identify the reactants and products

The reactants in this fission reaction are Uranium-235 (\(^{235}\mathrm{U}\)) and a neutron (\(^1\mathrm{n}\)). The products, as mentioned above, will be Barium-144 (\(^{144}\mathrm{Ba}\)), Krypton-90 (\(^{90}\mathrm{Kr}\)), and three additional neutrons (\(^1\mathrm{n}\)).

Write down the nuclear symbols

Using atomic symbols and mass numbers, we can write the nuclear equation as: \(^{235}\mathrm{U} + ^1\mathrm{n} \rightarrow ^{144}\mathrm{Ba} + ^{90}\mathrm{Kr} + 3\,^1\mathrm{n}\)

Check if the equation is balanced

To check if the equation is balanced, we need to ensure that the total atomic number (the number of protons) and the total mass number (the sum of protons and neutrons) are conserved in the reaction. For the reactants, we have \(^{235}\mathrm{U}\) with 92 protons and \(^1\mathrm{n}\) with zero protons: Total atomic number (Protons) = 92 Total mass number (Protons + Neutrons) = 235 + 1 = 236 For the products, we have \(^{144}\mathrm{Ba}\) with 56 protons, \(^{90}\mathrm{Kr}\) with 36 protons, and three neutrons (mass number is equal to the number of neutrons as they have no protons): Total atomic number (Protons) = 56 + 36 = 92 Total mass number (Protons + Neutrons) = 144 + 90 + 3 = 236 + 1 = 237 The total atomic number and mass number for reactants and products are the same, so the equation is balanced. The nuclear fission equation for the bombardment of Uranium-235 by neutrons can be written as: \(^{235}\mathrm{U} + ^1\mathrm{n} \rightarrow ^{144}\mathrm{Ba} + ^{90}\mathrm{Kr} + 3\,^1\mathrm{n}\)

Key concepts

uranium-235

Uranium-235, commonly written as \(^{235}\mathrm{U}\), is a naturally occurring isotope of uranium. It is very important in nuclear physics due to its unique property of being fissile. Fissile materials can undergo nuclear fission, meaning they can be split into smaller parts when hit by a neutron.

U-235 makes up about 0.7% of natural uranium, while the most abundant isotope is Uranium-238, which cannot sustain a chain reaction as easily.
This makes U-235 precious and useful in nuclear reactors and weapons. In reactors, it is used as a fuel to produce energy, as when it splits, it releases a tremendous amount of energy in the form of heat.

This released energy is harnessed to produce electricity in nuclear power plants. Additionally, a byproduct of its fission is more neutrons, which can cause further fission reactions, maintaining a chain reaction.

nuclear equation

In nuclear physics, equations represent nuclear reactions. These reactions involve changes in the nucleus of the atom rather than its electrons, and a nuclear equation is used to express this transformation.

For the nuclear fission reaction involving Uranium-235, the reaction can be typically written as:
\[^{235} \mathrm{U} + ^1 \mathrm{n} \rightarrow ^{144} \mathrm{Ba} + ^{90} \mathrm{Kr} + 3 \,^1 \mathrm{n}\]

This reaction highlights the splitting of the uranium nucleus into smaller nuclei. In this reaction, Uranium-235 absorbs a neutron and becomes unstable. Consequently, it splits into Barium-144 and Krypton-90, releasing additional neutrons and energy in the process.

• The reactants are on the left side of the equation and include Uranium-235 and a neutron.
• The products on the right are Barium-144, Krypton-90, and three more neutrons.

These equations must be carefully balanced to conserve both mass numbers and atomic numbers, ensuring an accurate description of the reaction.

neutron bombardment

Neutron bombardment is a critical process in initiating nuclear reactions, especially fission. This process involves a neutron colliding with the nucleus of an atom, causing it to become unstable.

Specifically, for Uranium-235, introducing a neutron transforms the isotope into a short-lived, excited state. This excitation quickly results in the splitting of the nucleus, a process known as fission.

Neutron bombardment is precise; neutrons, being neutral in charge, can penetrate the nuclei of atoms without being repulsed by the positive charges in the nucleus.

• This makes them ideal for initiating nuclear reactions.
• In the case of nuclear reactors, the neutrons are often moderated or slowed down to increase the efficacy of the bombardment, thus maintaining the chain reaction smoothly.

Hence, understanding and managing neutron bombardment is essential for the safe and effective use of nuclear technology.

balanced nuclear reaction

In a balanced nuclear reaction, both the mass numbers (sum of protons and neutrons) and atomic numbers (protons) are conserved.

This adherence to conservation laws ensures that the equation accurately reflects the physical process occurring during the reaction. Ensuring that a nuclear equation is balanced requires careful accounting of every particle before and after the reaction.

In the case of Uranium-235's neutron bombardment reaction:

• The total atomic number on both sides is 92 (92 protons in Uranium-235 and the sum of protons in Barium-144 and Krypton-90).
• The total mass number on both sides of the equation remains 236, verifying that the reaction is balanced.

Balancing these reactions helps physicists understand how matter behaves on an atomic level and also ensures the accuracy and predictability of the reactions involved.