Problem 32 - Chemistry The Central Science In Si Units

Question

Write balanced equations for each of the following nuclear reactions: \((\mathbf{a}){ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U},(\mathbf{b}){ }_{8}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }^{13} \mathrm{~N},\) (c) \({ }_{8}^{18} \mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }_{9}^{19} \mathrm{~F} .\)

Step-by-Step Solution

Answer

(a) _{92}^{238} ext{U} + _{0}^{1} ext{n} ightarrow _{92}^{239} ext{U} + ext{γ}, (b) _{8}^{16} ext{O} + _{1}^{1} ext{p} ightarrow _{7}^{13} ext{N} + _{2}^{4} ext{He}, (c) _{8}^{18} ext{O} + _{0}^{1} ext{n} ightarrow _{9}^{19} ext{F} + eta^{-} + ar{ u}_{e}.

Step 1: Understand Reaction Types

(a) involves a neutron capture (n, γ), meaning a neutron is absorbed and a gamma ray is emitted. (b) is a proton-induced reaction that emits an alpha particle. (c) involves beta-minus decay (n, β⁻), where a neutron turns into a proton, emitting a beta particle and an antineutrino.

Step 1: Balance Reaction (a)

For the reaction \(_{92}^{238} ext{U}(n, ext{γ}) ext{U}_{92}^{239},\) the equation shows that uranium-238 captures a neutron to form uranium-239, emitting gamma radiation. Because a neutron is added, the atomic number stays the same, and the mass number increases by 1: \[{}_{92}^{238} ext{U} + {}_{0}^{1} ext{n} ightarrow {}_{92}^{239} ext{U} + ext{γ}.\] This is already balanced.

Step 2: Balance Reaction (b)

For \(_{8}^{16} ext{O}(p, ext{α}) ext{N}_{7}^{13},\) oxygen-16 interacts with a proton to yield nitrogen-13 and an alpha particle. Calculate the mass and atomic numbers: \[{}_{8}^{16} ext{O} + {}_{1}^{1} ext{p} ightarrow {}_{7}^{13} ext{N} + {}_{2}^{4} ext{He}.\] On the left, total mass is 17 and atomic number 9; on the right, 17 (13 + 4) and 9 (7 + 2) respectively. The equation is balanced.

Step 3: Balance Reaction (c)

For the reaction \(_{8}^{18} ext{O}(n, eta^{-}){}_{9}^{19} ext{F},\) oxygen-18 undergoes neutron capture to form fluorine-19 via beta decay. Thus: \[{}_{8}^{18} ext{O} + {}_{0}^{1} ext{n} ightarrow {}_{9}^{19} ext{F} + eta^{-} + ar{u}_{e}.\] The neutron contributes mass and the atomic number increases by 1 through beta-minus decay. Mass and atomic numbers reveal balance.

Key Concepts

Neutron Capture

In the realm of nuclear reactions, neutron capture is an intriguing process. Simply put, it's when an atomic nucleus absorbs a neutron and, in the process, emits a gamma ray. This is why it's often represented in nuclear equations as \((n, \gamma)\).
Neutron capture reactions are pivotal in understanding how different isotopes form.

Here's a quick example: when uranium-238 \(({}_{92}^{238}\mathrm{U})\) undergoes neutron capture, it absorbs the neutron \(({}_{0}^{1}\mathrm{n})\) to become uranium-239 \(({}_{92}^{239}\mathrm{U})\) while the gamma radiation \((\gamma)\) is emitted. The equation:

• \({}_{92}^{238}\mathrm{U} + {}_{0}^{1}\mathrm{n} \rightarrow {}_{92}^{239}\mathrm{U} + \gamma\)

is already balanced!
This process is crucial in nuclear reactors and the creation of heavy elements in stars. Understanding neutron capture helps us grasp nuclear synthesis and energy generation in the universe.

Beta Decay

Beta decay is a nuclear process where a neutron in an unstable nucleus converts into a proton. Consequently, a beta particle \((\beta^{-}\), an electron) and an antineutrino \((\bar{u}_{e})\) are emitted.
It's like an atomic transformation, allowing the atom to achieve a more stable configuration.

Consider oxygen-18 \(({}_{8}^{18}\mathrm{O})\) undergoing beta decay after capturing a neutron, forming fluorine-19 \(({}_{9}^{19}\mathrm{F})\). The reaction:

• \({}_{8}^{18}\mathrm{O} + {}_{0}^{1}\mathrm{n} \rightarrow {}_{9}^{19}\mathrm{F} + \beta^{-} + \bar{u}_{e}\)

reflects the emission of a beta particle and an increase in atomic number due to the newly formed proton.
Beta decay plays a significant role in radioactive decay chains and the conversion of one element into another, serving as a cornerstone for understanding nuclear stability.

Proton-Induced Reactions

Proton-induced reactions occur when a proton interacts with a nucleus, causing various nuclear transformations. One such type of reaction involves the emission of an alpha particle, a bundle of two protons and two neutrons \((\alpha)\), recognizable as \((p, \alpha)\).
Despite being somewhat lesser-known than other types of decay, they offer insight into nuclear reactions' dynamics.

Take for instance oxygen-16 \(({}_{8}^{16} \mathrm{O})\) reacting with a proton \(({}_{1}^{1} \mathrm{p})\) to produce nitrogen-13 \(({}_{7}^{13} \mathrm{N})\) and an alpha particle:\[

• \({}_{8}^{16} \mathrm{O} + {}_{1}^{1} \mathrm{p} \rightarrow {}_{7}^{13} \mathrm{N} + {}_{2}^{4} \mathrm{He}\)

\]Here, both mass and atomic numbers are preserved, ensuring the reaction is balanced.
Such reactions help in understanding nuclear absorption processes and particle physics, providing a deeper insight into the natural world.