Unit 13 Study Guide: Atomic Nuclei and Nuclear Chemistry

Atomic Nuclei and the Evolution of the Atomic Model

The study of atomic nuclei begins with a review of Rutherfords Gold Foil expierment and its role in overturning the "Plum Pudding" atomic model of atom. Through this experiment, it was discovered that the nucleus is the Positive center of the atom, which is characterized as being both tiny and dense. The results demonstrated that atoms are composed mostly of empty space, a discovery that contributed significantly to the identification of the nuueus.

Nuclide Representation and Nuclear Stability

Nuclei, also known as nuclides, can be represented in two distinct ways to define their composition. The first method uses the symbol (x) accompanied by the mass number (A) on the top left and the atomic number (Z) on the bottom left, notationally represented as ${}_Z^A X$. Here, the mass number A represents the total count of protons and neutrons, while the atomic number Z identifies the number of protons. The second method provides the element name followed by the mass number, such as Radium-228 or RG 228. For example, two isotopes of Tellurium can be represented based on their subatomic particles: ${}_{52}^{122} Te$ contains $52P$ (protons) and $70N$ (neutrons), whereas ${}_{52}^{124} Te$ contains $52P$ and $72N$.

Nuclear stability is governed by specific thresholds related to atomic size and mass. It is a general rule that nuclei possessing mass numbers greater than 209 (represented as $A > 209$) and atomic numbers greater than or equal to 83 (represented as $Z \geq 83$) are never stable. These unstable nuclei will undergo decay to reach a more balanced state.

Mechanisms of Radioactivity and Decay Types

Radioactivity is defined as the emission of particles and energy, specifically electromagnetic energy, in an effort to create a more stable nucleus. This process involves the conversion of mass into energy, as detailed in Reference Table O. There are several specific types of nuclear changes that occur during radioactive decay.

Beta Decay occurs when an isotope has too many neutrons. In this process, the nucleus converts neutrons into protons and emits a high-energy electron known as a beta particle. The general equation for this change is ${}_0^1 n \rightarrow {}_1^1 p + {}_{-1}^0 e$. Because a neutron is converted into a proton, the atomic number of the element increases. An example of this is the decay of Carbon-14: ${}_6^{14} C \rightarrow {}_7^{14} N + {}_{-1}^0 e$.

Election Capture and Gamma Radiation involve the conversion of protons into neutrons. If a nucleus has too many protons, it may capture an electron from the atom, which decreases the atomic number by one while the mass number stays the same. When the nucleus eventually stabilizes, it releases energy in the form of gamma rays. The governing equation is ${}_1^1 p + {}_{-1}^0 e \rightarrow {}_0^1 n + \gamma$.

Poistron Emission is utilized by some nuclei with an excess of protons to become stable. This process involves emitting poistrans, which are considered the antiparticles of electrons. Protons are converted to neutrons via the equation ${}_1^1 p \rightarrow {}_0^1 n + {}_{+1}^0 e$. An example provided is the decay of Chromium: ${}_{24}^{49} Cr \rightarrow {}_{23}^{49} V + {}_{+1}^0 e$.

Alpha Particle emission occurs in unstable nuclei that decay by emitting an alpha (a) particle, which is equivalent to a Helium-4 nucleus (${}_2^4 He$). An alpha particle has a mass of approximately $4.00147492$ amu and a charge of $+2$. During this emission, the atomic number decreases by two and the mass number decreases by four. For instance, the alpha decay of Uranium-238 is expressed as ${}_{92}^{238} U \rightarrow {}_{90}^{234} Th + {}_2^4 He$. Many heavy metals, including Uranium-238, go through a sequence of these reactions known as a decay series.

The Band of Stability and Particle Characteristics

Nuclear decay occurs in a manner that returns a nucleus to the Band of Stability, often referred to as the stability curve. For a nucleus to be considered stable, it must maintain a neutron-to-proton (n:p) ratio between $1.0$ and $1.5$. If the atomic number $Z \geq 83$, the nuclide is automatically considered radioactive. The primary modes of adjustment are beta decay (converting neutrons to protons), election capture and poistron emission (converting protons to neutrons), and alpha particle emission (the loss of a helium nucleus).

The properties of these particles dictate how they interact with matter and what materials can stop them. A Proton (${}_1^1 H$ or $p$) has a mass of $1.00727647$ amu and a $+1$ charge; it can be stopped by a few sheets of paper. A Neutron (${}_0^1 n$ or $n$) has a mass of $1.00866490$ amu and $0$ charge; it requires a few centimeters of lead to be stopped. A Beta particle (${}_{-1}^0 e$ or $\beta^-$) has a mass of $0.00054858$ amu and a $-1$ charge; it is stopped by a few sheets of aluminum foil. A Poistron (${}_{+1}^0 e$ or $\beta^+$) has the same mass as an electron and a $+1$ charge, with shielding needs similar to a beta particle. An Alpha particle (${}_2^4 He$ or $\alpha$) has a mass of $4.00147492$ amu and a $+2$ charge; it is stopped by a single sheet of paper. Finally, a Gamma ray ($\gamma$) has no mass ($0$) and no charge ($0$); it is the most penetrating, requiring $7\,cm$ of lead for shielding.

Transmutation and Balancing Nuclear Equations

Transmutation is a nuclear reaction where one element changes into another by altering the nucleus of an atom. This change cannot be achieved through ordinary chemical reactions. Spontaneous Natural transmutation does not require an outside energy source; it involves one atom on the left-hand side of the reaction forming multiple particles, such as the alpha decay of Uranium-235: ${}_{92}^{235} U \rightarrow {}_2^4 He + {}_{90}^{231} Th$. Artificial Transmutation requires an external energy source and involves multiple atoms or particles on the left-hand side of the reaction, such as neutron bombardment: ${}_7^{14} N + {}_2^4 He \rightarrow {}_8^{17} O + {}_1^1 H$.

When balancing nuclear equations, both the total mass and the total charge must always balance across the reaction. For example, in the decay ${}_{92}^{238} U \rightarrow {}_{90}^{234} Th + {}_2^4 He$, the mass balance is $238 = 234 + 4$ and the charge balance is $92 = 90 + 2$. In the beta decay of Thorium, ${}_{90}^{234} Th \rightarrow {}_{91}^{234} Pa + {}_{-1}^0 e$, the mass balance is $234 = 234 + 0$ and the charge balance is $90 = 91 + (-1)$. It is critical to remember that whenever the atomic number changes, the identity of the element also changes.

Half-Life and Radioactive Dating

Half-life is defined as the time required for half of a sample of a radioactive substance to disintegrate through radioactive decay or natural processes. The half-life of a radioactive isotope is a constant value that is not influenced by external conditions like temperature or pressure. A general rule is that the more unstable a nuclide is, the shorter its half-life and the faster it decays.

Radioactive decay is used for various purposes including smoke detectors, art forgeries, medicine, and geologic dating. Potassium-40 ($K-40$) has a half-life of $1.2 \times 10^9$ (1.2 billion) years and decays via ${}_{19}^{40} K \rightarrow {}_{18}^{40} Ar + {}_{+1}^0 e$ or ${}_{19}^{40} K \rightarrow {}_{20}^{40} Ca + {}_{-1}^0 e$. It is used to determine the age of ancient rocks and minerals. Carbon-14 is used for dating things that were once living. Nearly all carbon on Earth is stable Carbon-12, but a small percentage in the crust is Carbon-14, which has a half-life of $5715$ years and decays via ${}_6^{14} C \rightarrow {}_7^{14} N + {}_{-1}^0 e$.

To calculate remaining mass over time, one applies the half-life. Starting with $100\,g$ of C-14, after one half-life ($5715$ years), $50\,g$ remains. After three half-lives ($17,145$ years), the remaining amount is $1/2 \times 1/2 \times 1/2 \times 100 = 12.5\,g$. After five half-lives ($28,575$ years), the amount remaining is $1/2 \times 1/2 \times 1/2 \times 1/2 \times 1/2 \times 100 = 3.125\,g$.

Fission and Fusion Reactions

Fission is the process of splitting the nucleus of a large atom into two or more smaller fragments. An example is ${}_{92}^{235} U + {}_0^1 n \rightarrow {}_{36}^{93} Kr + {}_{56}^{140} Ba + 3 {}_0^1 n$. Most fission reactions are artificial, achieved by bombarding nuclei with neutrons. This can lead to chain reactions that continue until no radioactive material capable of undergoing fission remains. In nuclear reactors, these chain reactions are controlled to produce large amounts of energy.

Fusion involves the combination of the nuclei of small atoms to form a larger nucleus. Fusion reactions release significantly greater amounts of energy than fission reactions for the same mass of starting material. However, fusion requires extremely high temperatures ($4 \times 10^7 \, ^\circ C$) to bring nuclei together. Currently, the only places where fusion reactions naturally occur are in stars.

Key Radioisotopes and Their Applications

Certain radioisotopes are essential for specific tasks in medicine and industry. Iodine-131 (I-131) is used for treating thyroid aliments, while Carbon-14 (C-14) is for carbon dating once-living things. Uranium-238 (U-238) decaying to Lead-206 (Pb-206) is used for rock dating. Cobalt-60 (Co-60) is prominent in cancer treatment, and Technetium-99 (Tc-99) is used for tumor detection. Phosphorus-31 (P-31) serves as a tracer for the uptake of phosphorus in plants, and Uranium-235 (U-235) is used as nuclear reactor fuel.