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The Aufbau Principle and Hund's Rule03:02

The Aufbau Principle and Hund's Rule

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To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the...
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Electron Configurations02:46

Electron Configurations

26.9K
Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
The relative energies of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p,...
26.9K
Electron Orbital Model01:18

Electron Orbital Model

74.3K
Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
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Atomic Orbitals02:44

Atomic Orbitals

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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
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Atomic Emission Spectroscopy: Overview01:20

Atomic Emission Spectroscopy: Overview

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Atomic emission spectroscopy (AES) is an analytical technique used to determine the elemental composition of a sample by analyzing the light emitted from excited atoms. In AES, atoms in a sample are excited to higher energy levels by thermal energy from high-temperature sources, such as plasma, arcs, or sparks. When these excited atoms return to lower energy states, they emit light at specific wavelengths characteristic of each element. The resulting atomic emission spectrum, which consists of...
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Electronic Structure of Atoms02:28

Electronic Structure of Atoms

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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Related Experiment Video

Updated: Feb 25, 2026

Microscopic Visualization of Porous Nanographenes Synthesized through a Combination of Solution and On-Surface Chemistry
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Microscopic Visualization of Porous Nanographenes Synthesized through a Combination of Solution and On-Surface Chemistry

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Shape-Dependent Single-Electron Levels for Au Nanoparticles.

Georgios D Barmparis1,2, Georgios Kopidakis3,4, Ioannis N Remediakis5,6

  • 1Department of Materials Science and Technology, University of Crete, 71003 Heraklion, Greece. barmparis@physics.uoc.gr.

Materials (Basel, Switzerland)
|August 5, 2017
PubMed
Summary
This summary is machine-generated.

We developed a method to determine nanoparticle shape using quantum energy levels. This technique reveals distinct electronic features crucial for designing better catalysts for heterogeneous catalysis and photocatalysis.

Keywords:
goldmaterial designnanomaterialsnanoparticlessingle-electron states

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A Continuous-flow Photocatalytic Reactor for the Precisely Controlled Deposition of Metallic Nanoparticles
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A Continuous-flow Photocatalytic Reactor for the Precisely Controlled Deposition of Metallic Nanoparticles
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Area of Science:

  • Surface Science
  • Computational Chemistry
  • Materials Science

Background:

  • Nanoparticle shape significantly impacts catalytic and photocatalytic performance.
  • Understanding shape-dependent electronic properties is key to catalyst design.
  • Current methods for shape determination can be limited.

Purpose of the Study:

  • To propose a novel method for determining nanoparticle shape.
  • To investigate the relationship between nanoparticle shape and electronic structure.
  • To provide insights for designing advanced catalysts.

Main Methods:

  • Solving the Schrödinger equation for nanoparticles of arbitrary shapes.
  • Utilizing single-electron quantum level measurements for shape determination.
  • Employing Wulff construction based on first-principles calculations for realistic gold nanoparticle models.

Main Results:

  • The proposed method accurately predicts energy levels for high-symmetry shapes (cube, sphere).
  • Distinct shape-dependent features in single-electron levels and density of states were observed for gold nanoparticles.
  • Surface coverage (clean, CO, thiolate) influences electronic structure, shifting energy levels towards spherical or cubic characteristics.

Conclusions:

  • Single-electron quantum levels offer a sensitive probe for nanoparticle shape.
  • Shape-dependent electronic structure variations can be experimentally identified.
  • This approach can guide the rational design of heterogeneous and photocatalytic materials.