Atomic physics - Atomic Structure and Quantum Models

Isolated Atoms and Atomic Processes Why We Model Atoms as Isolated In gases and plasmas, atoms are far apart from each other. The time it takes for two atoms to collide and interact is much longer than the time it takes for processes to occur within a single atom (like an electron jumping between energy levels). This means we can treat each atom as if it's completely alone—without worrying about nearby atoms interfering. This is the key assumption that allows us to use simple atomic models. When modeling what happens inside an atom, we focus on the nucleus (positively charged) surrounded by one or more electrons (negatively charged) held in place by the electric force. These bound electrons cannot escape to infinity unless they gain enough energy. Three Fundamental Atomic Processes An isolated atom can undergo three basic processes when it absorbs energy. Understanding these is essential because they explain what happens to electrons and what light the atom emits or absorbs. Ionization occurs when an electron absorbs enough energy to escape the atom completely. The energy required to remove an electron from the atom is called the binding energy. Once an electron absorbs energy equal to or greater than its binding energy, it leaves the atom, creating a positively charged ion. Excitation occurs when an electron absorbs energy, but not enough to escape. Instead, it jumps to a higher energy level (an excited state) while remaining bound to the nucleus. This is like climbing a staircase—the electron goes from one defined energy step to another, but stays in the building. De-excitation is the reverse: an excited electron spontaneously drops back down to a lower energy level. When this happens, the atom releases the energy difference as a photon—a packet of light. The energy of the photon depends only on which two energy levels are involved: $E{\text{photon}} = E{\text{upper}} - E{\text{lower}}$ A key point: excitation, ionization, and de-excitation can happen either through light absorption/emission (radiative processes) or through collisions with other particles (collision-induced processes). The Bohr Model of Hydrogen The Basic Picture The Bohr model provides a simple but remarkably accurate description of hydrogen atoms (and other single-electron atoms like singly-ionized helium). In this model, an electron orbits the nucleus in one of several allowed circular orbits. These orbits are stable—unlike classical physics would predict, an electron moving in a circular orbit does not radiate energy and spiral into the nucleus. Quantization: The Key Innovation The crucial insight of Bohr's model is that not all orbits are allowed. Instead, only certain discrete orbits satisfy a quantization condition. Specifically, the angular momentum of an electron must satisfy: $$L = n\hbar$$ where $n$ is a positive integer (1, 2, 3, ...), and $\hbar$ (called "h-bar") is the reduced Planck constant. The integer $n$ is called the principal quantum number, and each allowed value corresponds to one energy level. What does this mean physically? The electron can occupy the $n=1$ level (closest to nucleus, lowest energy), the $n=2$ level, the $n=3$ level, and so on. But it cannot occupy orbits in between these—the energy levels are discrete (separate, not continuous). This quantization is the profound departure from classical physics. Why This Matters: Spectral Lines Because only certain energy levels are allowed, an electron can only absorb or emit very specific amounts of energy. When an electron in a low energy level absorbs a photon with exactly the right energy, it jumps to a higher level. This is absorption. The photon must have energy equal to the difference between the two levels. When an electron in a high energy level drops to a lower level, it emits a photon with energy equal to that energy difference. This is emission. The result? Each atom produces a unique pattern of light colors (spectral lines) that acts like an atomic fingerprint. This is why we can identify which elements are present in distant stars—their light contains their characteristic spectral lines. Important Limitation The Bohr model works well for hydrogen-like atoms—atoms with only one electron (hydrogen itself, or ionized helium with one electron removed, etc.). For atoms with multiple electrons, this simple circular-orbit model breaks down. We need more sophisticated quantum mechanics to describe them properly. Electronic Configuration in Complex Atoms Electron Shells and Ground State When atoms have multiple electrons, we imagine them occupying different shells (or subshells) around the nucleus, each at a different distance and energy. The ground state is the configuration where all electrons occupy the lowest-energy shells available. Atoms naturally prefer the ground state because systems naturally move toward the lowest energy. If you provide energy to an atom, you can excite electrons to higher shells, but they will eventually drop back down to the ground state, emitting light in the process. Binding Energy and Ionization Each electron is held in its shell by the attractive electric force from the nucleus. The binding energy of an electron is the energy required to remove that electron to infinity (far away from the atom). An important point: when a photon or particle delivers energy to an electron, if that energy is less than the binding energy, excitation occurs. If it's equal to or greater than the binding energy, ionization occurs. Any energy in excess of the binding energy becomes kinetic energy of the departing electron: $$E{\text{absorbed}} = E{\text{binding}} + KE{\text{electron}}$$ Notice that binding energy depends on which shell the electron is in. Electrons close to the nucleus (inner shells) are bound more tightly and have higher binding energies. Outer electrons are easier to remove. X-rays and the Auger Effect When an inner electron is knocked out (ionized), a vacancy is created in that inner shell. An outer electron can fall down and fill that vacancy, emitting a photon in the process. These photons are often in the X-ray region of the spectrum, so they're called characteristic X-rays—each element produces X-rays of characteristic energies. There's another possibility: instead of emitting a photon, the energy released when an outer electron fills an inner vacancy can be transferred directly to another electron, which is then ejected from the atom. This process is called the Auger effect. Why does this matter? The Auger effect allows a single photon (say, an X-ray) to cause multiple ionizations in an atom. First, it knocks out one electron. Then, as the vacancy is filled, another electron gets ejected via the Auger process. This cascading effect creates highly ionized (multiply-charged) atoms—an important process in plasma physics. Selection Rules for Transitions Light-induced transitions (absorption and emission) follow selection rules—mathematical restrictions on which transitions are allowed. These rules come from the detailed quantum mechanics of atoms and relate to properties of the electronic states. However, here's the important distinction: these selection rules only apply to light-induced transitions. When electrons collide with other particles rather than absorbing photons, the selection rules don't apply. Collision-induced transitions can happen between any states, regardless of selection rules. This is practically important: in a plasma with many collisions, you can have transitions that light alone could never cause. This affects what light gets emitted from the plasma. <extrainfo> Additional detail about selection rules: The most common selection rule for light-induced transitions involves orbital angular momentum. Generally, when an atom absorbs or emits light, the orbital angular momentum quantum number ($\ell$) must change by 1. Transitions that violate this rule (like $\ell$ staying the same) are called "forbidden" and happen with very low probability through light, but can happen readily through collisions. </extrainfo>