Physics

# Section Summary

PhysicsSection Summary

### 22.1The 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 $ΔE= E i − E f ΔE= E i − E f$, where $E n = Z 2 n 2 E o ( n=1,2,3,... ) E n = Z 2 n 2 E o ( n=1,2,3,... )$ .
• The wavelength of energy absorbed or emitted by an electron as it changes energy state can be determined by the equation $1 λ =R( 1 n f 2 − 1 n i 2 ) 1 λ =R( 1 n f 2 − 1 n i 2 )$, where $R=1.097× 10 7 m −1 R=1.097× 10 7 m −1$ .
• Described as an electron cloud, the quantum model of the atom is the result of de Broglie waves and Heisenberg’s uncertainty principle.

• 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 $X Z A N → Y Z−2 A−4 N + H 2 4 e X Z A N → Y Z−2 A−4 N + H 2 4 e$ .
• 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 $X Z A N → Y Z+1 A N−1 +e+v X Z A N → Y Z+1 A N−1 +e+v$ . (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 $X Z A N → X N +γ X Z A N → X N +γ$ .
• The penetration distance of radiation depends on its energy, charge, and type of material it encounters.

### 22.3Half Life and Radiometric Dating

• 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 $R= ΔN Δt R= ΔN Δt$ .
• 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 $N= N O e −λt N= N O e −λt$ .
• 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.

### 22.4Nuclear Fission and Fusion

• 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 $E=m c 2 E=m c 2$ .
• 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).