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Related Concept Videos

¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...
Nuclear Stability03:18

Nuclear Stability

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
To hold positively charged protons together in the...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
Quantum Numbers02:43

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

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Related Experiment Video

Updated: Jun 5, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Pions in large N quantum chromodynamics.

Steven Weinberg1

  • 1Department of Physics, University of Texas, Austin, Texas 78712, USA. weinberg@physics.utexas.edu

Physical Review Letters
|January 15, 2011
PubMed
Summary

This study proposes an effective field theory for quarks, gluons, and pions, simplifying calculations for hadronic phenomena. The theory is renormalizable and effective at moderate energies, offering new avenues for research.

Area of Science:

  • Theoretical Particle Physics
  • Quantum Chromodynamics
  • Hadronic Phenomena

Background:

  • Quantum Chromodynamics (QCD) describes strong interactions but is complex at moderate energies.
  • The large N limit (where N is the number of colors) offers a simplification but has limitations.

Purpose of the Study:

  • To develop an effective field theory (EFT) for quarks, gluons, and pions.
  • To enable calculations of hadronic phenomena at moderate energies using a large N approach.
  • To explore the implications of constituent quark masses in the EFT.

Main Methods:

  • Formulating an effective field theory with N colors treated as large.
  • Incorporating constituent quark masses into the effective Lagrangian.
  • Analyzing the theory's behavior at moderate energies and to leading order in 1/N.

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Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping
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Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

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Last Updated: Jun 5, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

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Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping
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Main Results:

  • The proposed EFT provides a basis for calculating hadronic phenomena.
  • Qualitative consequences of the large N limit are observed, similar to pure QCD.
  • The 't Hooft coupling in the effective theory does not require strong coupling at moderate energies.
  • The theory is renormalizable to leading order in 1/N, with a finite number of Lagrangian terms.

Conclusions:

  • The effective field theory offers a tractable approach to studying hadronic phenomena.
  • The inclusion of constituent quark masses modifies the behavior of the large N limit.
  • The EFT's renormalizability and finite terms simplify calculations in theoretical particle physics.