Question

U-2 35 undergoes many different fission reactions. For one such reaction, when U- 235 is struck with a neutron, Ce- 144 and Sr90 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 of U-235 involving the production of Ce-144 and Sr-90, there are 2 neutrons (\(n\)) and 4 beta particles (\(\beta^{-}\)) produced.

Step-by-step solution

Identify the reactants and products

The reactants are: - U-235 (an isotope of Uranium) as the target nucleus - Neutron that strikes U-235 The products are: - Ce-144 (an isotope of Cerium) - Sr-90 (an isotope of Strontium) - Unknown number of neutrons - Unknown number of beta particles The fission reaction can be represented as: \[n + _{92}^{235}U \rightarrow _{58}^{144}Ce + _{38}^{90}Sr + x\, n + y\, \beta^{-}\]

Apply conservation of nucleon number

The total number of nucleons (protons + neutrons) should be the same before and after the reaction. Since U-235 has 235 nucleons and the incoming neutron has 1, the total nucleon number on the left is 236. In the equation below, x is the number of neutrons and A1, A2 represent the nucleon numbers for Ce-144 and Sr-90, respectively: \[236 = A_1 + A_2 + x\] Since both A1 and A2 are known: A1 = 144 and A2 = 90, we can write: \[236 = 144 + 90 + x\]

Solve for the unknown number of neutrons x

Now, it's time to solve the equation for x: \[x = 236 - 144 - 90\] \[x = 2\] So, 2 neutrons are produced in this fission reaction.

Apply conservation of charge

The total charge on both sides of the reaction should be conserved. The initial charge on the left side is from U-235 itself since the incoming neutron has no charge. On the right side, y beta particles are produced. β⁻ particles are electrons, so each has a charge of -1. The equation can be written as: \[92 = 58 + 38 - y\]

Solve for the unknown number of Beta particles y

Now, we can solve the equation for y: \[y = 58 + 38 - 92\] \[y = 4\] So, 4 beta particles are produced in this fission reaction. In conclusion: In this fission reaction, when U-235 is struck with a neutron and results in the production of Ce-144 and Sr-90, there are 2 neutrons and 4 beta particles produced.

Key concepts

Uranium-235

Uranium-235, often abbreviated as U-235, is a significant isotope of uranium, a naturally occurring element. It is known for its role in nuclear reactors and atomic bombs due to its ability to sustain chain reactions through nuclear fission. U-235 has 92 protons and 143 neutrons, giving it a mass number of 235. This makes it both unstable and susceptible to fission when it absorbs a neutron.
One of the key properties of U-235 is its ability to undergo fission by capturing a neutron. This reaction releases a significant amount of energy and additional neutrons, which can then induce fission in other U-235 nuclei, thus maintaining a chain reaction.
Key points about Uranium-235:

• Composed of 92 protons and 143 neutrons
• Capable of sustaining a nuclear chain reaction
• Produces substantial energy when it undergoes fission

Understanding these properties helps to explain why U-235 is valuable for both energy production and weaponry.

neutron production

Neutron production is crucial in the context of nuclear fission, especially regarding isotopes like Uranium-235. During the fission process, U-235 absorbs an additional neutron, becoming unstable, and subsequently splits into smaller nuclei, such as Cerium-144 and Strontium-90, as noted in the exercise.
The splitting of U-235 releases free neutrons along with energy. These free neutrons are essential as they can trigger fission in other U-235 nuclei, creating a chain reaction. The number of neutrons produced during fission varies, but in this specific reaction, two neutrons are generated.
Key aspects of neutron production:

• Free neutrons released are crucial for sustaining fission reactions
• Each fission event of U-235 typically releases two or three neutrons

Understanding neutron production helps manage nuclear reactions, ensuring they are controlled effectively in reactors.

beta particles

Beta particles play a significant role in nuclear reactions, particularly during the decay process. In the context of the exercise, beta particles emerge from the conservation of charge during the fission process of U-235.
A beta particle is essentially a high-energy, high-speed electron or positron emitted from the radioactive decay of an atomic nucleus. In beta-minus decay, a neutron is transformed into a proton, emitting an electron (beta particle) and an antineutrino. Regarding this specific fission reaction, four beta particles are produced as a result of charge conservation on both sides of the reaction equation.
Important points about beta particles:

• They are electrons (beta-minus) or positrons (beta-plus) emitted from decaying nuclei
• Involve the transformation of a neutron into a proton during beta-minus decay
• Help balance the charge during nuclear fission processes

Grasping the concept of beta particles facilitates understanding of nuclear reactions and the balancing of atomic equations.

nucleon conservation

Nucleon conservation is a fundamental principle in nuclear physics, ensuring that the total number of nucleons remains constant during a nuclear reaction. Nucleons include protons and neutrons, and their conservation is essential for balancing nuclear equations.
In the given exercise, nucleon conservation plays a crucial role in determining the number of neutrons produced. Initially, the sum of nucleons from U-235 and an additional neutron results in a total of 236 nucleons. Post-fission, this total must still equate to 236, split among the produced Cerium-144, Strontium-90, and any additional neutrons.
Key points on nucleon conservation:

• Ensures total nucleon count remains constant before and after nuclear reactions
• Essential for accurately balancing nuclear equations and predicting reaction products
• Helps identify neutron production based on nucleon accounting

Understanding nucleon conservation is fundamental to solving complex nuclear reactions and ensures accuracy in nuclear equations.