22.1 The Structure of the Atom

Rutherford’s gold foil experiment provided evidence that the atom is composed of a small, dense nucleus with electrons occupying the mostly empty space around it.
Analysis of emission spectra shows that energy is emitted from energized gas in discrete quantities.
The Bohr model of the atom describes electrons existing in discrete orbits, with discrete energies emitted and absorbed as the electrons decrease and increase in orbital energy.
The energy emitted or absorbed by an electron as it changes energy state can be determined with the equation $Δ E = E_{i} - E_{f}$ , where $E_{n} = \frac{Z^{2}}{n^{2}} E_{o} (n = 1, 2, 3, ...)$ .
The wavelength of energy absorbed or emitted by an electron as it changes energy state can be determined by the equation $\frac{1}{λ} = R (\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}})$ , where $R = 1.097 \times 10^{7} m^{−1}$ .
Described as an electron cloud, the quantum model of the atom is the result of de Broglie waves and Heisenberg’s uncertainty principle.

22.2 Nuclear Forces and Radioactivity

The structure of the nucleus is defined by its two nucleons, the neutron and proton.
Atomic numbers and mass numbers are used to differentiate between various atoms and isotopes. Those numbers can be combined into an easily recognizable form called a nuclide.
The size and stability of the nucleus is based upon two forces: the electromagnetic force and strong nuclear force.
Radioactive decay is the alteration of the nucleus through the emission of particles or energy.
Alpha decay occurs when too many protons exist in the nucleus. It results in the ejection of an alpha particle, as described in the equation ${}_{Z}^{A}X_{N} \to {}_{Z - 2}^{A - 4}Y_{N} + {}_{2}^{4}H e_{}$ .
Beta decay occurs when too many neutrons (or protons) exist in the nucleus. It results in the transmutation of a neutron into a proton, electron, and neutrino. The decay is expressed through the equation ${}_{Z}^{A}X_{N} \to {}_{Z + 1}^{A}Y_{N - 1} + e + v$ . (Beta decay may also transform a proton into a neutron.)
Gamma decay occurs when a nucleus in an excited state move to a more stable state, resulting in the release of a photon. Gamma decay is represented with the equation ${}_{Z}^{A}X_{N} \to X_{N} + γ$ .
The penetration distance of radiation depends on its energy, charge, and type of material it encounters.

Radioactive half-life is the time it takes a sample of nuclei to decay to half of its original amount.
The rate of radioactive decay is defined as the sample’s activity, represented by the equation $R = \frac{Δ N}{Δ t}$ .
Knowing the half-life of a radioactive isotope allows for the process of radioactive dating to determine the age of a material.
If the half-life of a material is known, the age of the material can be found using the equation $N = N_{O} e^{- λ t}$ .
The age of organic material can be determined using the decay of the carbon-14 isotope, while the age of rocks can be determined using the decay of uranium-238.

Nuclear fission is the splitting of an atomic bond, releasing a large amount of potential energy previously holding the atom together. The amount of energy released can be determined through the equation $E = m c^{2}$ .
Nuclear fusion is the combining, or fusing together, of two nuclei. Energy is also released in nuclear fusion as the combined nuclei are closer together, resulting in a decreased strong nuclear force.
Fission was used in two nuclear weapons at the conclusion of World War II: the gun-type uranium bomb and the implosion-type plutonium bomb.
While fission has been used in both nuclear weapons and nuclear reactors, fusion is capable of releasing more energy per reaction. As a result, fusion is a well-researched, if not yet well-controlled, energy source.

Medical imaging occurs when a radiopharmaceutical placed in the body provides information to an array of radiation detectors outside the body.
Devices utilizing medical imaging include the Anger camera, SPECT detector, and PET scan.
Ionizing radiation can both cure and cause cancer through the manipulation of DNA molecules.
Radiation dosage and its effect on the body can be measured using the quantities radiation dose unit (rad), relative biological effectiveness (RBE), and the roentgen equivalent man (rem).