Question

The number of neutrons accompanying the formation of \({ }_{54} \mathrm{Xe}^{139}\) and \({ }_{38} \mathrm{Sr}^{94}\) from the absorption of slow neutrons by \({ }_{92} \mathrm{U}^{235}\) followed by nuclear fission is (a) 0 (b) 2 (c) 1 (d) 3

Short answer

The number of neutrons produced is (d) 3.

Step-by-step solution

Write the Fission Reaction

The nuclear reaction involves Uranium-235 \(({}^{235}_{92} \text{U})\) absorbing a neutron \((n)\), which then undergoes fission to form Xenon-139 \(({}_{54}\text{Xe}^{139})\) and Strontium-94 \(({}_{38}\text{Sr}^{94})\), along with some additional neutrons. The balanced fission reaction can be expressed as: \[ {}^{1}_{0}n + {}^{235}_{92}U \rightarrow {}_{54}\text{Xe}^{139} + {}_{38}\text{Sr}^{94} + xn \] Here, \(xn\) represents the additional neutrons produced in the reaction.

Check Atomic Numbers and Mass Numbers

To balance the nuclear reaction, ensure the sum of atomic numbers and mass numbers on both sides is equal. - Atomic numbers: \(92 + 0 = 54 + 38 + 0\). - Mass numbers: \(235 + 1 = 139 + 94 + x\).

Solve for Neutron Difference

Using the balanced equation for mass numbers: \[ 236 = 233 + x \] Solve for \(x\): \[ x = 236 - 233 = 3 \] Thus, 3 neutrons are produced in the reaction.

Verifying Atomic Number Balance

Since the mass number balance is achieved, we check that the atomic numbers also match: \[ 92 + 0 = 54 + 38 \] This confirms that the balanced reaction produces 3 additional neutrons without affecting the stability of atomic numbers.

Key concepts

Uranium-235

Uranium-235 is a highly significant isotope in the world of nuclear energy. It is one of the few materials that can undergo induced fission, making it a key player in both nuclear reactors and weapons. When a neutron is absorbed by Uranium-235, it becomes Uranium-236, an unstable isotope. This instability causes the Uranium-236 to split, or fission, into smaller fragments.

In nuclear fission, Uranium-235 is specifically desirable due to its ability to sustain a chain reaction. It can release a large amount of energy, along with producing additional free neutrons that can further perpetuate the process. These features are crucial for the self-sustaining chain reactions required in reactors.

• Uranium-235 can undergo fission after capturing a neutron.
• This process is accompanied by the release of energy.
• Fulfills a critical role in nuclear power generation and weaponry.

Neutron Emission

During the fission of Uranium-235, neutrons play a crucial role in both initiating and continuing nuclear reactions. When Uranium-235 absorbs a neutron and undergoes fission, the atomic nucleus splits into smaller nuclei – in this case, previously identified as Xenon-139 and Strontium-94.

This splitting also releases additional neutrons, which were represented as "xn" in the fission equation of the exercise. These neutrons are not just excess byproducts; they are critical to sustaining further nuclear reactions. Each emitted neutron has the potential to cause additional Uranium-235 atoms to fission, leading to a chain reaction.

• Neutrons initiate the fission process by absorption.
• Additional neutrons are released during fission.
• Neutron emission sustains nuclear chain reactions, making it essential for ongoing energy release.

Atomic Number Balance

In nuclear reactions, maintaining a balance of atomic numbers is crucial to ensuring that the reaction is accurately represented and understood. The atomic number tells us the number of protons in a nucleus and hence defines the element. In the fission reaction involving Uranium-235, we must ensure that the sum of atomic numbers on the reactant side equals that on the product side.

Here's how atomic balance was verified in the exercise:

• The atomic number of Uranium is 92.
• On the product side, we have Xenon with an atomic number of 54 and Strontium with 38.
• This yields a total atomic number of 92 (54+38) on the product side, which equals the atomic number of Uranium.

This balance confirms that the identities of the elements involved in the reaction are preserved, an essential factor in accurate nuclear reaction equations.

Mass Number Conservation

Mass number conservation in nuclear reactions ensures that the total number of protons and neutrons remains the same before and after the reaction. Mass numbers are the sum of protons and neutrons in a nucleus. Although the actual mass isn't perfectly conserved due to the conversion of some mass into energy (as described by Einstein’s famous equation, \(E=mc^2\)), the total mass number on both sides of the equation should remain equal.

In our exercise, this is demonstrated as follows:

• The combined mass number on the reactant side is 236 (Uranium-235 + 1 neutron).
• The combined mass number on the product side includes the mass numbers of Xenon-139, Strontium-94, plus some additional neutrons.
• Subsequently, it was calculated that 3 neutrons are needed to balance the mass numbers, maintaining a total mass number of 236 on both sides.

This is vital for ensuring the integrity and accuracy of nuclear equations.