Question

Write balanced equations for (a) \({ }_{92}^{238} \mathrm{U}(\alpha, \mathrm{n}){ }_{94}^{241} \mathrm{Pu},\) (b) \({ }_{7}^{14} \mathrm{~N}(\alpha, \mathrm{p}){ }^{17} \mathrm{O}\) (c) \({ }_{26}^{56} \mathrm{Fe}(\alpha, \beta)_{29}^{60} \mathrm{Cu}\).

Short answer

The balanced nuclear equations for the given reactions are as follows: (a) \({}_{92}^{238}\mathrm{U} + {}_{2}^{4}\mathrm{\alpha} \rightarrow {}_{94}^{241}\mathrm{Pu} + {}_{0}^{1}\mathrm{n}\) (b) \({}_{7}^{14}\mathrm{N} + {}_{2}^{4}\mathrm{\alpha} \rightarrow {}_{8}^{17}\mathrm{O} + {}_{1}^{1}\mathrm{p}\) (c) \({}_{26}^{56}\mathrm{Fe} + {}_{2}^{4}\mathrm{\alpha} \rightarrow {}_{29}^{60}\mathrm{Cu} + {}_{-1}^{0}\mathrm{\beta}\)

Step-by-step solution

(a) Balancing the Uranium Reaction:

For \({}_{92}^{238}\mathrm{U}(\alpha, \mathrm{n}){}_{94}^{241}\mathrm{Pu}\), we need to balance the atomic numbers and mass numbers on both sides of the reaction. 1. Identify the alpha particle, which has an atomic number of 2 and a mass number of 4: \({}_{2}^{4}\mathrm{\alpha}\). 2. Identify the neutron, which has an atomic number of 0 and a mass number of 1: \({}_{0}^{1}\mathrm{n}\). 3. Write down the reaction with atomic and mass numbers: \({}_{92}^{238}\mathrm{U} + {}_{2}^{4}\mathrm{\alpha} \rightarrow {}_{94}^{241}\mathrm{Pu} + {}_{0}^{1}\mathrm{n}\). 4. Check if the atomic numbers and mass numbers are balanced: - Atomic numbers: 92 + 2 = 94 - Mass numbers: 238 + 4 = 241 + 1 The reaction is balanced.

(b) Balancing the Nitrogen Reaction:

For \({}_{7}^{14}\mathrm{N}(\alpha, \mathrm{p}){}^{17}\mathrm{O}\), we need to balance the atomic numbers and mass numbers on both sides of the reaction. 1. Identify the alpha particle, which has an atomic number of 2 and a mass number of 4: \({}_{2}^{4}\mathrm{\alpha}\). 2. Identify the proton, which has an atomic number of 1 and a mass number of 1: \({}_{1}^{1}\mathrm{p}\). 3. Write down the reaction with atomic and mass numbers: \({}_{7}^{14}\mathrm{N} + {}_{2}^{4}\mathrm{\alpha} \rightarrow {}_{8}^{17}\mathrm{O} + {}_{1}^{1}\mathrm{p}\). 4. Check if the atomic numbers and mass numbers are balanced: - Atomic numbers: 7 + 2 = 8 + 1 - Mass numbers: 14 + 4 = 17 + 1 The reaction is balanced.

(c) Balancing the Iron Reaction:

For \({}_{26}^{56}\mathrm{Fe}(\alpha, \beta)_{29}^{60}\mathrm{Cu}\), we need to balance the atomic numbers and mass numbers on both sides of the reaction. 1. Identify the alpha particle, which has an atomic number of 2 and a mass number of 4: \({}_{2}^{4}\mathrm{\alpha}\). 2. Identify the beta particle (electron), which has an atomic number of -1 and a mass number of 0: \({}_{-1}^{0}\mathrm{\beta}\). 3. Write down the reaction with atomic and mass numbers: \({}_{26}^{56}\mathrm{Fe} + {}_{2}^{4}\mathrm{\alpha} \rightarrow {}_{29}^{60}\mathrm{Cu} + {}_{-1}^{0}\mathrm{\beta}\). 4. Check if the atomic numbers and mass numbers are balanced: - Atomic numbers: 26 + 2 = 29 - 1 - Mass numbers: 56 + 4 = 60 The reaction is balanced.

Key concepts

Balancing Chemical Equations

Balancing chemical equations is like solving a puzzle where each piece must fit perfectly. In nuclear reactions, just like in regular chemical reactions, it is vital to ensure that both sides of the reaction have the same number of each type of atom. To balance a nuclear equation, you must balance both atomic numbers and mass numbers.

• Atomic Number: Represents the number of protons in the nucleus, determining the element's identity.
• Mass Number: The total of protons and neutrons in the nucleus, indicating the isotope's mass.

In any balanced equation, the sum of atomic numbers and mass numbers on the reactant side must equal the sum on the product side. For example, in reactions involving Uranium-238 and alpha particles, balancing ensures that the formation of a new element like Plutonium is energetically viable and follows the laws of conservation. Each reaction step needs to adhere strictly to these rules to be considered balanced.

Alpha Particles

Alpha particles are a type of ionizing radiation ejected by the nuclei of certain unstable atoms. They are composed of 2 protons and 2 neutrons, making them identical to a helium-4 nucleus. This gives them an atomic number of 2 and a mass number of 4. In nuclear reactions, alpha particles play a significant role in transmuting elements.
When an alpha particle is emitted during a nuclear reaction, it causes the parent nucleus to lose 2 protons and 2 neutrons. This leads to a decrease in the atomic number by 2 and the mass number by 4. This transformation is often used in nuclear equations where radioactive decay processes occur, such as when Uranium-238 decays into Thorium-234. The simplicity and predictability of alpha decay make it a foundational concept in nuclear chemistry.

Atomic Number

The atomic number of an element is a unique identifier that denotes the number of protons present in the nucleus of its atoms. It is this number, rather than the atomic mass, that determines the chemical behavior of an element. In the context of nuclear reactions, the atomic number is crucial for understanding the identity and transformation of elements.
In balancing nuclear equations, maintaining consistency in atomic numbers across reactants and products is essential. This ensures that the conservation of charge is observed. For instance, if we observe a nuclear process resulting in the emission of an alpha particle, the atomic number of the resulting product will decrease by two, reflecting the loss of two protons, as seen when balancing reactions involving Uranium or Nitrogen. This approach is key to predicting the outcomes and by-products of nuclear transformations.

Mass Number

The mass number is an important concept in nuclear chemistry, representing the total count of protons and neutrons in an atom's nucleus. This total gives insight into the actual mass of a specific isotope of an element. Unlike the atomic number, which defines the element, the mass number differentiates between different isotopes of the same element.
In nuclear reactions, balancing the mass number involves ensuring that the sum of protons and neutrons remains constant throughout the process. For example, when balancing the reaction of Nitrogen-14 with an alpha particle, the combined mass of the reactants must equal the products, including any neutrons or other particles involved. This principle helps chemists and physicists accurately depict reactions and avoid mistakes in predicting products' isotopes.