Question

\({ }_{2} \mathrm{U}^{235}\) nucleus absorbs a neutron and disintegrates into \({ }_{54} \mathrm{Xe}^{139},{ }_{38} \mathrm{Sr}^{94}\) and \(\mathrm{x}\). What will be the product \(\mathrm{x} ?\) (a) 3 neturons (b) 2 neturons (c) \(\alpha\) particle (d) \(\beta\) particle

Short answer

The product x is 3 neutrons.

Step-by-step solution

Understand the Nuclear Reaction

The problem involves a nuclear reaction where a Uranium-235 nucleus absorbs a neutron and subsequently undergoes fission to form Xenon-139, Strontium-94, and another product (\(x\)). This product could be additional neutrons or particles.

Analyze Atomic and Mass Numbers

In a nuclear reaction, both the mass number and the atomic number are conserved. Uranium-235 ( _{92} U^{235} ) absorbs a neutron ( _{0} n^{1} ) to become _{92} U^{236} . This fission results in the creation of Xenon ( _{54} Xe^{139} ) and Strontium ( _{38} Sr^{94} ).

Calculate Mass Number Balance

Calculate the mass number balance: 235 (Uranium) + 1 (neutron) = 139 (Xenon) + 94 (Strontium) + x (unknown) 236 = 233 + x, so x must be 3 to balance the mass numbers.

Calculate Atomic Number Balance

Calculate the atomic number balance: 92 (Uranium) = 54 (Xenon) + 38 (Strontium) + x (unknown) 92 = 92, which confirms our neutron hypothesis since we've accounted for the Xenon and Strontium atomic numbers.

Determine the Unknown Product

Since both mass number and atomic number balance indicate that x must be 3 in terms of mass number (as neutrons contribute only to the mass number and not to the atomic number), the unknown product is most likely neutrons. This eliminates the other particle options (alpha or beta particles) based on given choices.

Key concepts

Uranium-235

Uranium-235 is a very important isotope when discussing nuclear fission. Fission is the process where the nucleus of an atom splits into two or more smaller nuclei. This happens here when Uranium-235 absorbs a neutron. The significant point about Uranium-235 is that it is one of the few materials that can undergo induced fission. When it absorbs a neutron, it becomes unstable and splits.

In this particular reaction, Uranium-235 first absorbs an additional neutron, making it Uranium-236. This new Uranium-236 is unstable and quickly fissions, meaning it breaks down into smaller elements, releasing energy and additional particles, such as neutrons.

• It's an isotope of uranium, consisting of 92 protons and 143 neutrons.
• It plays a crucial role in nuclear reactors and atomic bombs.
• Known for its ability to sustain a nuclear chain reaction.

The ability of Uranium-235 to sustain chain reactions makes it essential in both the development of nuclear energy and nuclear weapons.

Mass Number Conservation

Mass number conservation is a key concept in nuclear reactions. The mass number refers to the total number of protons and neutrons in an atomic nucleus. In nuclear reactions, including fission, the sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products. This law points to the idea that matter is neither created nor destroyed in nuclear processes.

In the example given, the Uranium-235 (with a mass number of 235) absorbs a neutron with a mass number of 1, making the total mass number 236 before the fission occurs. The products, Xenon-139 and Strontium-94, together have a mass number of 233. This leaves us with missing mass numbers of 3, which indicates that three additional particles, such as neutrons, are present in the products.

• Mass number balances like this help identify unknown particles in nuclear reactions.
• It's crucial for confirming the accuracy of a nuclear reaction equation.

This helps us understand that, although atoms in the nucleus are rearranged or changed, the total amount remains constant.

Atomic Number Conservation

Atomic number conservation is another fundamental principle of nuclear reactions. The atomic number represents the number of protons in the nucleus of an atom. This is crucial because it defines the element itself. Just like mass number conservation, atomic number conservation means that the total atomic number before a nuclear reaction is equal to the total atomic number after the reaction.

In the steps outlined, the atomic number for Uranium is 92. Despite the fission and its transformation through a reaction with a neutron, the total atomic number of the products, which are Xenon with an atomic number of 54 and Strontium with 38, sums to 92. This shows that nothing was lost from the nuclei besides particles like neutrons, which don't affect atomic numbers.

• Atomic number conservation ensures the identity of the resulting elements.
• It's essential for checking the completion and correctness of nuclear reactions.

Understanding this principle clarifies why only neutrons, and no proton-carrying particles, account for changes in this reaction.