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Chemical Formulas02:52

Chemical Formulas

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A chemical formula presents information about the proportions of atoms constituting a particular chemical compound or molecule, mainly using symbols of elements and numbers. At times other symbols, such as dashes, parentheses, brackets, commas, plus, and minus signs, are also used. A chemical formula can be one of three types – molecular, empirical, and structural.
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Ionic Compounds: Formulas and Nomenclature03:34

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An element composed of atoms that readily lose electrons (a metal) can react with an element composed of atoms that readily gain electrons (a nonmetal) to produce ions through complete electron transfer. The compound formed by this transfer is stabilized by the electrostatic attractions (ionic bonds) between the oppositely charged ions.
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Molecular Compounds: Formulas and Nomenclature03:10

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Molecular compounds or covalent compounds result when atoms share electrons to form covalent bonds. Since there is no electron transfer, molecular compounds do not contain ions; instead, they consist of discrete, neutral molecules. 
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Experimental Determination of Chemical Formula02:37

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The elemental makeup of a compound defines its chemical identity, and chemical formulas are the most concise way of representing this elemental makeup. When a compound’s formula is unknown, measuring the mass of its constituent elements is often the first step in determining the formula experimentally.
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Formula Mass of Covalent Compounds
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Determining the Empirical Formula07:05

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Source: Laboratory of Dr. Neal Abrams - SUNY College of Environmental Science and Forestry
Determining the chemical formula of a compound is at the heart of what chemists do in the laboratory every day. Many tools are available to aid in this determination, but one of the simplest (and most accurate) is the determination of the empirical formula. Why is this useful? Because of the law of conservation of mass, any reaction can be followed gravimetrically, or by change in mass. The empirical...
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Updated: Jan 20, 2026

Chemical Formulas: Molecular, Empirical, Structural; Writing Formulas
02:52

Chemical Formulas: Molecular, Empirical, Structural; Writing Formulas

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Defect Verlinde Formula for Edge Excitations in Topological Order.

Ce Shen1, Ling-Yan Hung1

  • 1State Key Laboratory of Surface Physics, Fudan University, 200433 Shanghai, China, Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China, and Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, 200433 Shanghai, China.

Physical Review Letters
|September 7, 2019
PubMed
Summary

Researchers derived a formula relating boundary excitation fusion rules and half-linking numbers in topological orders. This advances understanding of topological phases and quantum computing platforms.

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Area of Science:

  • Condensed matter physics
  • Topological quantum matter

Background:

  • Topological orders in 2+1 dimensions exhibit exotic properties.
  • Boundary excitations and defects are crucial for understanding topological phases.

Purpose of the Study:

  • To derive a general formula for boundary excitations in nonchiral bosonic topological orders.
  • To establish a connection between fusion rules and topological properties like half-linking numbers.
  • To explore applications in quantum computing.

Main Methods:

  • Physical considerations to derive a formula analogous to the Verlinde formula.
  • Calculation of half-linking numbers for condensed anyons and boundary excitations.
  • Explicit computation for Abelian and non-Abelian topological orders.

Main Results:

  • A formula relating fusion rules of boundary excitations to the half-linking number is derived.
  • The half-linking number quantifies the interaction between condensed anyons and confined boundary excitations.
  • Demonstrated computation of these numbers in concrete examples.

Conclusions:

  • The derived formula provides a fundamental insight into topological orders and their boundaries.
  • The results have potential applications in designing and realizing quantum computing devices.
  • Understanding boundary phenomena is key to harnessing topological properties for quantum information processing.