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Atomic Orbitals

Atomic Orbitals

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.

Molecular Orbital Theory II

Molecular Orbital Theory II

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Molecular Orbital Theory I

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Hybridization of Atomic Orbitals II

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Electron Orbital Model

Electron Orbital Model

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...

Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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Related Experiment Video

Updated: Jan 20, 2026

Molecular Orbital MO Theory: Predicting Geometry of Transition Metal Complexes

Molecular Orbital MO Theory: Predicting Geometry of Transition Metal Complexes

Published on: April 30, 2023

Capillary orbits.

Anaïs Gauthier¹, Devaraj van der Meer², Jacco H Snoeijer³

¹Physics of Fluids Group and Max Plank Center Twente. Mesa + Institute and Faculty of Science and Technology, J.M. Burgers Centre for Fluid Dynamics and Max Plank Center Twente for Complex Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands. anais.gauthier@espci.fr.

Nature Communications

|September 4, 2019

Summary

This summary is machine-generated.

Objects on liquid surfaces attract each other due to surface distortion, a phenomenon known as the Cheerios effect. This study observed levitating droplets orbiting due to this capillary attraction, offering insights into self-assembly and cryopreservation.

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Last Updated: Jan 20, 2026

Molecular Orbital MO Theory: Predicting Geometry of Transition Metal Complexes

Molecular Orbital MO Theory: Predicting Geometry of Transition Metal Complexes

Published on: April 30, 2023

Atomic Orbitals: Radial Distribution Function, Nodes and Shapes

Atomic Orbitals: Radial Distribution Function, Nodes and Shapes

MO Diagrams, Bond Order, MO Theory and Bonding in Benzene

MO Diagrams, Bond Order, MO Theory and Bonding in Benzene

Area of Science:

Physics
Colloid Science
Surface Science

Background:

Objects on liquid surfaces create capillary waves, leading to attractive forces.
The Cheerios effect explains clumping in everyday scenarios and has potential for self-assembly.
Levitating droplets in an inverse Leidenfrost state offer a unique, low-friction environment to study these forces.

Purpose of the Study:

To investigate capillary attraction between levitating droplets.
To analyze droplet dynamics shaped solely by the Cheerios-interaction potential.
To explore applications in contactless, contamination-free cryopreservation.

Main Methods:

Creating levitating droplets in an inverse Leidenfrost state above liquid nitrogen.
Observing and analyzing the orbital trajectories of these droplets.
Deriving the Cheerios-interaction potential directly from observed droplet dynamics.

Main Results:

Levitating droplets spontaneously orbited each other, forming a miniature celestial system.
Droplet trajectories were exclusively governed by the Cheerios-interaction potential due to negligible friction.
The study quantified the interaction potential from experimental dynamics.

Conclusions:

The Cheerios effect governs droplet interactions in a low-friction environment.
This phenomenon can be harnessed for controlled self-assembly of colloidal particles.
Synergistic use of the Leidenfrost effect and capillarity offers novel cryopreservation methods.