Section X - exam III

System: is a collection of particles that interact among themselves via internal forces and that may interact with the world outside via external fields.
intrinsic properties: These don’t depend on the particle’s location, don’t evolve with time, and aren’t influenced by its physical environment (e.g., rest mass and charge).
Extrinsic Properties: These evolve with time in response to the forces on the particle (e.g., position and momentum).
State: Listing values of the observables of a particle at any time
Trajectory: the values of its position and momentum for all times after some initial (arbitrary) time t◦) of a particle:
Determinate universe: knowing the initial conditions of the constituents of any system, however complicated, we can use Newton’s Laws to predict the future.
Principle of causality: If the Universe is determinate, then for every effect there is a cause
Wave-particle duality: The concept of a particle doesn’t exist in the quantum world — so-called particles behave both as a particle and a wave
Heisenberg Uncertainty Principle: This is not just a matter of experimental uncertainties, nature itself will not allow position and momentum to be resolved to infinite precision
Correspondence principle:Since Newtonian (i.e., mechanics) and Maxwellian (i.e., thermodynamics) physics describe the macroscopic world so well, physicists developing quantum mechanics demanded that when applied to macroscopic systems, the new physics must reduce to the old physics. coined by neils bohr.
Quantum chromodynamics: When we are in the realm of the nucleus (i.e., distances less than 10−14 m), the laws of (nuclear) physics are described with
Strong interactions: force that binds nucleons together.
Hadrons: participate in strong interactions.
E/M interactions: force between charged particles.
Weak interactions: These are responsible for radioactive decay of nuclei.
Gravitational interactions: Attractive force between bodies with mass.
Elementary particles: These are particles that make up matter. They are subdivided into 3 groups: leptons, mesons, and baryons.
Leptons: (light particles) are low mass particles. These particles do not participate in the strong interactions, but do interact with the other 3 natural forces. All leptons have spin of 1/2.
Mesons: are particles of intermediate mass that are made of quark-antiquark pairs and include pions, kaons, and η-particles. All are unstable and decay via weak or E/M interactions. All mesons have either 0 or integer spin.
Baryons: (heavy particles) include the nucleons n (neutrons — neutral particles) and p (protons — positive charged) and the more massive hyperons Donald G. Luttermoser, ETSU X–9 (i.e., Λ, Σ,Ξ, and Ω). Baryons are composed of a triplet of quarks. Each baryon has an antibaryon associated with it with a spin of either 1/2 or 3/2.
Field particles: These particles mediate the 4 natural forces as mentioned above: gluons, photons, weakons, and gravitons. These are the energy particles.
Wave function: The wave function describes the quantum state of a system, encapsulating all information about a particle's position, momentum, and spin, which can be used to predict the probabilities of various outcomes during measurement. a system of identical particles.
Symmetrical wave function: In quantum mechanics, a symmetrical wave function is one that remains unchanged under the exchange of two identical particles, ensuring that the overall quantum state respects the indistinguishability principle.
anti-symmetrical wave function: An anti-symmetrical wave function, in contrast, changes sign when two identical fermions are exchanged, reflecting the Pauli exclusion principle that states no two fermions can occupy the same quantum state simultaneously.
Bosons: Symmetrical and can have zero or integer spins.
Fermions: anti-symmetrical and have half integer spins.
Pauli Exclusion Principle: An antisymmetrical wave function must vanish as 2 identical particles approach each other. As a result, 2 fermions in the same quantum state exhibit a strong mutual repulsion
Quantum states: As mentioned above, the energy, orbital angular momentum, and spin angular momentum do not vary in a continuous way for electrons that are bound in atoms and molecules. Instead, they can only have values that are quantized =⇒ electrons can only “orbit” the nucleus of an atom in allowed states known as
electronic configuration: each element / ion has an __________________ associated with it, which is based on the periodic table. Each e − in that configuration has a characteristic set of quantum numbers.
electronic configuration (n): principal quantum number =⇒ shell ID. n = 1,2,3,4, etc….
electronic configuration (L): orbital angular momentum quantum number =⇒ subshell ID. l = 0, 1, 2, 3, etc… subshell = s,p,d, f etc….
electronic configuration (s): spin angular momentum quantum number =⇒ spin direction (i.e., up or down).
element: We have seen that atoms consist of a central nucleus composed of protons.
isotope: We have seen that atoms consist of a central nucleus composed of which defines the isotope
bound-bound transition state: If a photon collides with an atom, an electron can jump from one bound level to another if the energy of the photon matches the energy difference of the two states
excited state: an electron occupies a higher energy level than its ground state, leading to potential transitions that can result in the emission or absorption of light.
absorption: The process by which an atom takes in a photon, causing an electron to transition from a lower energy level to a higher energy level, resulting in a temporary excited state.
spontaneous emission: the process by which an excited electron returns to a lower energy level, resulting in the release of a photon and the emission of light. Results from HUP
stimulated emission: the process by which an incoming photon interacts with an excited electron, causing it to drop to a lower energy level while simultaneously releasing a second photon that is coherent with the first. results from nearby E/M field i.e, another photon or nearby atom.
emission: The process by which a material releases energy in the form of photons, which can occur in both spontaneous and stimulated forms, playing a crucial role in various physical phenomena.
scattering: photon can be re-emitted in any direction. As such, it might not return to the original path that it had before the interaction. Hence, this would also produce an absorption line if viewed from the outside.
ionization: If a high-energy photon (one whose energy exceeds the ionization potential) interacts which an atom, the electron can be completely “ripped” off the atom
recombination: The process in which free electrons combine with ions to form neutral atoms, often resulting in the emission of energy in the form of photons, thereby influencing the surrounding environment and contributing to phenomena such as nebulae formation.
Lyman series: Lines that originate from (or terminate to) the same level in a hydrogen-like atom/ion are said to belong to the same series. Transitions out of (or into) the ground state (n = 1) are lines of the________.
Balmer series: The Balmer series refers to the set of spectral lines corresponding to electron transitions from higher energy levels to the second level (n = 2) in hydrogen, which fall within the visible spectrum.
Paschen series: The Paschen series consists of spectral lines that arise from electron transitions from higher energy levels to the third energy level (n = 3) in hydrogen, which primarily fall within the infrared region of the electromagnetic spectrum.
resonance lines: Lines that go into or come out of the ground state are referred to as
ionization potential: defined as the amount of energy required to remove an electron from an atom or ion in its gaseous state, leading to the formation of a positively charged ion. n → infinity
ground state: lowest energy state ( E = 0)
series limit: The series limit refers to the highest energy level an electron can achieve, corresponding to the transition where the electron is completely removed from the atom. ionization “edge” of the series in a spectrum.
state: A term used to describe the various energy levels that electrons can occupy within an atom, where each state corresponds to specific electron configurations and energy levels.
Bohr radius: The Bohr radius is the average distance between the nucleus and the electron in a hydrogen atom in its ground state, often denoted as 'a0', and represents the scale of atomic structures.
oscillator strength: The oscillator strength is a dimensionless quantity that represents the probability of an electron transitioning between energy levels, indicating the strength of absorption or emission of light in an atom or molecule.
allowed transition: refers to an electron's transition between energy levels that is permitted by the selection rules, resulting in observable spectral lines in absorption or emission spectra. occurs only if one electron changes a bound state, typically the outermost valence electron.
semiforbidden transition: will occur if either the spin rule or the orbital angular momuntum rule is violated. Such a transition has a low probability of occurring. Such transitions are typically seen in low density gas such as the outer atmospheres of stars.
forbidden transition: will occur if both the spin rule and the orbital angular momuntum rule are violated. Such a transition has an extremely low probability of occurring. Such transitions are only seen in rarified gas. Forbidden lines are common in the interstellar medium (i.e., the gas in interstellar space) due to its very low density.
spectroscopic notation: these transitions are typically represented by specific quantum states, allowing for the identification of unique spectral lines that highlight the presence of various elements within the gas.
metastable states: The other lower energy states labelled with an ‘a’ are referred to as ____________ since they act like the ground state (though have higher energies than the ground state).
multiplet numbers: These are used to indicate the number of closely spaced energy levels that result from the interactions between quantum states, providing insight into the complexity of the spectral lines observed in the interstellar medium.