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5: Electrons in Atoms

Last updated

Mar 21, 2025
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- 4.20: Calculating Average Atomic Mass
- 5.1: Electromagnetic Spectrum

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5.1: Electromagnetic Spectrum
This page discusses the nature of waves, highlighting that they represent energy beyond just water. It critiques Rutherford's atomic model for not addressing electron behavior and notes early 20th-century experiments showcasing light's dual wave-particle nature. Additionally, it details visible light's wavelength (400-700 nm) and speed (3.
5.2: Wavelength and Frequency Calculations
This page discusses the enjoyment of beach activities along with the risks of UVB exposure, emphasizing the necessity of sunscreen. It explains wave characteristics such as wavelength and frequency, introducing the formula $c = \lambda \nu$ that relates them. An example calculation for the frequency of orange light is included to illustrate the application of the formula. The summary highlights key wave properties and their definitions.
5.3: Quantization of Energy
This page clarifies that "quantum leap" refers to minor changes in an electron's position, not significant breakthroughs. It highlights Max Planck's discovery that energy emits in discrete units called quanta, opposing classical physics' continuous energy view. A quantum is the smallest energy change for an atom, defined by Planck's constant $h = 6.626 \times 10^{-34} \: \text{J} \cdot \text{s}$ . This principle is fundamental for understanding energy behavior at the atomic level.
5.4: Photoelectric Effect
This page explores the development of solar sails for spacecraft propulsion, a concept from 1950s science fiction. It explains Einstein's 1905 proposal of light's particle nature, leading to the photoelectric effect, where light ejects electrons from metal surfaces based on frequency. Only light above a certain threshold can cause this ejection, with higher frequencies enhancing electron speed. The photoelectric effect has practical applications in devices such as calculators.
5.5: Atomic Emission Spectra
This page explains the principles of energy conversion through archery, where kinetic energy is transformed to potential energy and back to kinetic energy upon release. It parallels atomic emission spectra, where energy excites electrons in an atom, leading to light emission at specific wavelengths when they return to lower energy states. This quantized behavior challenges classical physics and aligns with quantum theory.
5.6: Bohr's Atomic Model
This page explores the analogy of climbing a ladder to explain potential energy and Niels Bohr's 1915 atomic model, where electrons occupy fixed energy states around the nucleus. It describes how electrons can gain or emit energy, often as light, when transitioning between these states. While effective for hydrogen, the model's limitations with other elements led to revisions in atomic theory.
5.7: Spectral Lines of Atomic Hydrogen
This page discusses the evolution of scientific theory through automobile repairs and the Bohr model of the hydrogen atom. It highlights how energy changes in a hydrogen atom create spectral lines linked to electron transitions, successfully explaining the hydrogen emission spectrum but revealing limitations for multi-electron atoms. Key concepts include energy level quantization, the Balmer series, and the need for advancements in atomic theory.
5.8: de Broglie Wave Equation
This page discusses Bohr's atomic model and its limitations regarding electron orbits. It highlights the work of Louis de Broglie, who introduced the wave nature of particles, showing that electrons behave with dual characteristics. De Broglie's equation allows for the calculation of an electron's wavelength, indicating that a decrease in speed results in an increased wavelength.
5.9: Quantum Mechanics
This page delves into quantum mechanics, highlighting the dual wave-particle nature of atomic and subatomic particles. It contrasts quantum mechanics with classical mechanics, focusing on discrete energy changes (quanta) and the fundamental uncertainty in electron positioning, which is addressed through probabilities. Prominent physicists like Niels Bohr and Richard Feynman stressed the baffling aspects of quantum theory, emphasizing its challenge to traditional concepts in physics.
5.10: Heisenberg Uncertainty Principle
This page discusses practical applications of lasers in construction for precise measurements and their role in measuring the Earth-Moon distance. It also explains the Heisenberg Uncertainty Principle, highlighting the challenge of simultaneously knowing a particle's position and velocity due to measurement disturbances at the atomic level, unlike larger objects where such effects are minimal.
5.11: Quantum Mechanical Atomic Model
This page discusses the quantum mechanical model of the atom, introduced by Erwin Schrödinger in 1926. It highlights the shift from fixed electron orbits in the Bohr model to electron probabilities within a diffuse "electron cloud." The concept of orbitals represents areas with a 90% chance of finding electrons, showcasing the model's emphasis on uncertainty and the probabilistic nature of electron location.
5.12: Energy Level
This page explains how fireworks create colorful bursts of light through energy transitions of electrons in atoms. It outlines electron shells' roles in determining energy levels, and highlights that valence electrons impact an atom's stability and reactivity. Reactive elements with incomplete valence shells, like fluorine and lithium, contrast with the stability of neon, which has a full outer shell.
5.13: Orbitals
This page discusses electron configurations and orbitals defined by quantum numbers, detailing the four types: $s$ (spherical), $p$ (dumbbell-shaped), $d$ (complex), and $f$ (most complex, with seven shapes). It also compares the regulations preventing plane collisions to the restrictions on electron positioning.
5.14: Quantum Numbers
This page explains quantum numbers that characterize electrons in atoms, detailing four types: the principal quantum number (n) for energy levels, the angular momentum quantum number (l) for orbital shape, the magnetic quantum number (m_l) for orbital orientation, and the spin quantum number (m_s) for electron spin. These quantum numbers collectively define an electron's unique state within an atom.
5.15: Aufbau Principle
This page explains the Aufbau principle, which dictates that electrons fill atomic orbitals starting from the lowest energy level to the highest. It details the organization and filling of atomic sublevels, beginning with $1s$ and moving through $2s$ , $2p$ , $3s$ , and beyond. The text highlights the overlap in sublevel energies, particularly with the $3d$ and $4s$ orbitals, and discusses exceptions to the typical filling order.
5.16: Pauli Exclusion Principle
This page explores the concept of unique identification by comparing email addresses to how electrons are distinguished by quantum numbers. It elaborates on the Pauli exclusion principle, which states that no two electrons can share the same set of four quantum numbers. As a result, when three quantum numbers match, the fourth—spin—must differ, allowing each orbital to hold two electrons with opposing spins, illustrated through the example of helium.
5.17: Hund's Rule and Orbital Filling Diagrams
This page explains Hund's rule, emphasizing the need for single occupancy of degenerate orbitals before pairing to reduce repulsion among electrons. It introduces orbital filling diagrams that depict electron arrangements, using arrows to indicate spin. Examples from boron, carbon, nitrogen, and oxygen illustrate how electrons fill sublevels according to the Aufbau principle, highlighting the process of electron arrangement in atoms.
5.18: Electron Configurations
This page explains electron configurations as a simplified notation for representing electron arrangements in atoms, using superscripts to denote electrons in occupied sublevels. An example of carbon illustrates this with a configuration of $1s^2 2s^2 2p^2$ . It also lists second period elements and their configurations, showcasing the filling of $s$ and $p$ sublevels in the periodic table. The summary highlights the clarity and simplicity of this notation.
5.19: Valence Electrons
This page explains valence electrons as the outermost electrons in an atom's highest energy level, which determine reactivity. It highlights that elements react differently based on their valence electron count, with lithium having one, beryllium two, and boron three. As one progresses across a period, valence electrons increase, reaching eight in neon. The summary also distinguishes between valence and inner shell electrons, noting that only valence electrons affect reactivity.
5.20: Noble Gas Configuration
This page discusses noble gas configurations in electron configurations, likening full outer electron shells of noble gases to the feeling of fullness after eating. It covers sodium's electron configuration and introduces shorthand notation using noble gas symbols for simplification. The approach applies to subsequent periods, referencing various noble gases. The text ends with review questions on specific configurations.

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