Question

Write balanced equations for each of the following nuclear reactions: (a) \({ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma)^{239} \mathrm{G}_{2} \mathrm{U}\), (b) \({ }_{7}^{14} \mathrm{~N}(\mathrm{p}, \alpha){ }_{6}^{11} \mathrm{C}\), (c) \({ }^{18} \mathrm{O}(\mathrm{n}, \beta)_{9}^{19} \mathrm{~F}\).

Short answer

The balanced nuclear reactions are: (a) \[{}_{92}^{238}\mathrm{U} + {}_{0}^{1}\mathrm{n} \rightarrow {}_{92}^{239}\mathrm{U} + {}_{0}^{0}\gamma\] (b) \[{}_{7}^{14}\mathrm{N} + {}_{1}^{1}\mathrm{p} \rightarrow {}_{6}^{11}\mathrm{C} + {}_{2}^{4}\mathrm{He\] (c) \[{}_{8}^{18}\mathrm{O} + {}_{0}^{1}\mathrm{n} \rightarrow {}_{9}^{19}\mathrm{F} + {}_{-1}^{0}\beta\]

Step-by-step solution

(a) Uranium-238 capturing a neutron and gamma radiation

In this reaction, a Uranium-238 nucleus captures a neutron and emits gamma radiation, forming Uranium-239. To balance the equation, we need to ensure the atomic numbers and mass numbers are the same on both sides of the equation. On the left side, we have Uranium-238 and a neutron, which can be represented as \(_{0}^{1}\mathrm{n}\). On the right side, we have Uranium-239 and gamma radiation, represented by \(_{0}^{0}\gamma\). The balanced equation is: \[ {}_{92}^{238}\mathrm{U} + {}_{0}^{1}\mathrm{n} \rightarrow {}_{92}^{239}\mathrm{U} + {}_{0}^{0}\gamma \]

(b) Nitrogen-14 reacting with a proton to form Carbon-11 and an alpha particle

In this reaction, Nitrogen-14 reacts with a proton and forms Carbon-11 and an alpha particle. A proton is represented as \(_{1}^{1}\mathrm{p}\) and an alpha particle as \(_{2}^{4}\mathrm{He}\). To balance this equation, we need to ensure that the atomic numbers and mass numbers on both sides of the equation are equal. The balanced equation is: \[ {}_{7}^{14}\mathrm{N} + {}_{1}^{1}\mathrm{p} \rightarrow {}_{6}^{11}\mathrm{C} + {}_{2}^{4}\mathrm{He} \]

(c) Oxygen-18 capturing a neutron and undergoing beta decay to form Fluorine-19

In this reaction, Oxygen-18 captures a neutron and undergoes beta decay to form Fluorine-19. A neutron is represented as \(_{0}^{1}\mathrm{n}\), and a beta particle (electron) is represented as \(_{-1}^{0}\beta\). To balance this equation, ensure that the atomic numbers and mass numbers on both sides are equal. The balanced equation is: \[ {}_{8}^{18}\mathrm{O} + {}_{0}^{1}\mathrm{n} \rightarrow {}_{9}^{19}\mathrm{F} + {}_{-1}^{0}\beta \]

Key concepts

Balanced Equations

A balanced equation in nuclear reactions is similar to chemical equations but involves atomic and mass numbers. Every nuclear reaction must be balanced to satisfy the conservation of mass and charge.
In nuclear reactions, two types of balancing are required:

• Atomic numbers: These are the numbers of protons and must be the same on both sides of the equation.
• Mass numbers: These represent the total number of protons and neutrons, and must also match on both sides.

For example, in the given nuclear reaction of Uranium-238 capturing a neutron to form Uranium-239, the atomic and mass numbers are already balanced:

• Atomic numbers: Uranium (92) and neutron (0) become Uranium (92) and gamma (0), totaling 92 on both sides.
• Mass numbers: Uranium-238 and neutron (1) result in Uranium-239 and gamma (0), totaling 239 on both sides.

Ensuring accuracy in these calculations is crucial to understanding nuclear behavior and processes.

Gamma Radiation

Gamma radiation is a type of electromagnetic radiation emitted during nuclear reactions. It is represented by the symbol estatex{}{} in nuclear equations and has no mass or charge.
This form of radiation is particularly high energy and can penetrate most materials, making it useful but also potentially dangerous.
In nuclear reactions like the one with Uranium-238, gamma radiation is emitted when a nucleus transitions from a higher energy state to a lower energy state, maintaining the balance of the reaction without altering atomic or mass numbers.

• No effect on atomic number: \( \gamma \) radiation does not change the atomic number since it is chargeless.
• No effect on mass number: Since \( \gamma \) radiation is massless, the mass number remains unchanged.

This nature makes gamma rays ideal candidates for releasing excess energy in nuclear processes.

Beta Decay

Beta decay is a fundamental nuclear process where an unstable atomic nucleus transforms into a more stable one. During this process, a beta particle, which is either an electron or a positron, is emitted.
In the context of nuclear equations, beta decay is represented by the symbols \( {}_{-1}^{0}\beta \) for an electron or \( {}_{1}^{0}\beta \) for a positron.

• Impact on atomic number: When an electron (\( -1 \) atomic number) is emitted, the atomic number of the nucleus increases by 1, such as in the transition of Oxygen-18 to Fluorine-19.
• Effect on mass number: The mass number remains unchanged because a beta particle has negligible mass.

Beta decay is a critical feature of nuclear chemistry and physics, leading to transmutation where one element changes to another.

Atomic Numbers

The atomic number of an element is crucial because it defines the identity and number of protons within an atom’s nucleus.
In a nuclear equation, keeping track of atomic numbers helps in ensuring that reactions adhere to the law of conservation of charge.

• Symbol: The atomic number is often presented as a subscript on the left side of the chemical symbol in nuclear equations (e.g., \( {}_{92}^{238}\mathrm{U} \)).
• Determines the element: The atomic number differentiates one element from another due to the unique proton count.
• Impacted by reactions: While gamma radiation and alpha decay do not change atomic numbers, beta decay alters the atomic number by 1.

Understanding atomic numbers is foundational in describing how elements evolve through nuclear transformations.

Mass Numbers

Mass numbers are another critical component of nuclear reactions. The mass number is the sum of protons and neutrons within an atomic nucleus.

• Representation: Displayed as a superscript before the elemental symbol, it provides insight into isotopic identities (e.g., \( {}_{238}^{92}\mathrm{U} \)).
• Conservation in reactions: Mass numbers must be conserved, which is maintained in balanced nuclear equations like those involving neutrons, whereby the total mass remains constant.
• Role in identifying isotopes: Different isotopes of an element share the same atomic number but differ in mass numbers due to varied neutron counts.

Mastery of mass numbers allows for precise prediction and understanding of nuclear reactions, ensuring comprehensiveness in nuclear chemistry.