Question

Uranium- 235 undergoes many different fission reactions. For one such reaction, when \(^{235} \mathrm{U}\) is struck with a neutron, \(^{144} \mathrm{Ce}\) and \(^{90}\) Sr are produced along with some neutrons and electrons. How many neutrons and \(\beta\) -particles are produced in this fission reaction?

Short answer

In the fission reaction involving Uranium-235 that produces Cerium-144 and Strontium-90, 2 neutrons and 4 beta particles are produced.

Step-by-step solution

Write down the fission reaction

Begin by writing down the fission reaction. The given data can be represented as \[^{235}\mathrm{U} + ^1_0n \rightarrow ^{144}_{58}\mathrm{Ce} + ^{90}_{38}\mathrm{Sr} + x(^1_0n)+y( \beta)\] Here, we are given Uranium-235 (\(^{235}\mathrm{U}\)) is struck with a neutron (\(^1_0n\)) and we know it produces Cerium-144 (\(^{144}\mathrm{Ce}\)) and Strontium-90 (\(^{90}\mathrm{Sr}\)). We need to find the number of neutrons (\(x\)) and beta particles (\(y\)) produced in this reaction.

Apply the conservation of mass number

Start by applying the conservation of mass numbers. That means the sum of the mass numbers of reactants must be equal to the sum of the mass numbers of products. Therefore, \(235 + 1 = 144 + 90 + x\) Now, solve for the unknown "x": \(x = 235 + 1 - 144 - 90\) \(x = 236 - 234\) \(x = 2\) Thus, 2 neutrons are produced in this fission reaction.

Apply the conservation of atomic number

Now, apply the conservation of atomic numbers. That means the sum of the atomic numbers of reactants must be equal to the sum of the atomic numbers of products. Considering that beta particles have an atomic number of -1 as they tend to be electrons, the equation becomes: \(92 + 0 = 58 + 38 - y\) Now, solve for the unknown "y": \(y = 58 + 38 - 92\) \(y = 96 - 92\) \(y = 4\) Thus, 4 beta particles are produced in this fission reaction.

Final Answer

In the fission reaction involving Uranium-235 that produces Cerium-144 and Strontium-90, 2 neutrons and 4 beta particles are produced.

Key concepts

Conservation of Mass Number

Understanding the conservation of mass number is fundamental when analyzing nuclear reactions. In simple terms, the mass number is the total count of protons and neutrons in an atom's nucleus. During a nuclear fission reaction, like the one involving Uranium-235, this mass number must remain constant before and after the event.

In the given exercise, the mass numbers of the reacting Uranium-235 and the incoming neutron must equal the sum of the mass numbers of the produced elements and particles. By balancing the equation, students immediately see how mass is neither created nor destroyed in the process but simply redistributed, ensuring that the total number of nucleons (protons plus neutrons) stays the same. By working out the math, we can identify the number of neutrons produced in the fission reaction.

Conservation of Atomic Number

The conservation of atomic number is another indispensable law in nuclear physics, closely related to the charge conservation in physics. The atomic number, which is the number of protons in the nucleus, dictates an element's identity. During a nuclear reaction, while the protons might change in number due to processes like beta decay, the total charge before and after the reaction must remain constant.

Thus, when beta particles are emitted, they are considered to have an atomic number of -1 since they are essentially electrons ejected from the nucleus. This subtraction helps balance the atomic number in the fission equation, letting students find the number of beta particles emitted. This concept is crucial for students to understand elemental transmutation during nuclear reactions.

Beta Particles

Beta particles play a significant role in nuclear reactions and are a type of ionizing radiation. They are high-energy, high-speed electrons or positrons that are emitted by certain types of radioactive nuclei, such as Potassium-40. The release of beta particles is a byproduct of the beta decay process, wherein a neutron transforms into a proton or vice versa within an atom's nucleus.

Understanding beta particles helps explain changes in the atomic number during a nuclear fission reaction, as seen in the provided exercise, and why certain isotopes undergo beta decay. The characterization of these particles and their behaviors under different conditions is a topic of interest in nuclear chemistry and physics.

Neutron Interaction

Neutron interaction with the nucleus is the trigger for nuclear fission to occur. Neutrons are neutral particles that can easily penetrate the nucleus of atoms due to the absence of electric charge. When a neutron is absorbed by a fissile nucleus, like Uranium-235, it can destabilize it, causing the nucleus to split into smaller nuclei along with the release of additional neutrons and energy.

These additional neutrons can then propagate the reaction by interacting with other nuclei, which makes it a chain reaction. Understanding neutron interaction is pivotal when studying nuclear reactors and nuclear weapons, as the rate of these interactions determines the rate of energy production or the explosiveness of a weapon.