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Atomic Nuclei: Nuclear Spin State Population Distribution

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.

The Aufbau Principle and Hund's Rule

The Aufbau Principle and Hund's Rule

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 subshell of...

Electron Paramagnetic Resonance (EPR) Spectroscopy: Organic Radicals

Electron Paramagnetic Resonance (EPR) Spectroscopy: Organic Radicals

Ideally, an unpaired electron shows a single peak in the EPR spectrum due to the transition between the two spin energy states. However, coupling interactions can occur between the spins of the unpaired electron and any neighboring spin-active nuclei. This hyperfine coupling results in hyperfine splitting, where the EPR signal is split into multiplets. The signals split into 2nI + 1 peaks, where n is the number of equivalent nuclei and I is the nuclear spin. These splitting patterns provide...

Atomic Nuclei: Nuclear Spin State Overview

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...

Electron Configurations

Electron Configurations

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, 4s,...

Nuclear Stability

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...

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Related Experiment Video

Updated: Jun 19, 2026

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Published on: August 17, 2017

Hyperfine structure and absolute frequency of the (87)Rb 5P(3/2) state.

J Ye, S Swartz, P Jungner

|October 31, 2009

Summary

Two new (87)Rubidium D(2) spectrometers achieve high stability and reproducibility for atomic spectroscopy. This advancement significantly reduces uncertainty in measuring hyperfine constants for the 5P(3/2) state.

Area of Science:

Atomic Physics
Spectroscopy
Quantum Optics

Background:

Precise atomic spectroscopy is crucial for fundamental physics and quantum technologies.
Rubidium-87 (87Rb) is a key atom for atomic clocks and quantum information processing.

Purpose of the Study:

To construct and validate two independent, highly stable, and reproducible (87)Rb D(2) saturated-absorption spectrometers.
To improve the accuracy of hyperfine constant measurements for the 5P(3/2) state of (87)Rb.

Main Methods:

Development of two distinct spectrometer designs utilizing dither/third-harmonic lock-in detection and radio-frequency sideband techniques.
Achieved +/-3-kHz reproducibility and agreement between the two independent systems.
Employed heterodyne measurements to probe hyperfine splittings.

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Hyperpolarized Xenon for NMR and MRI Applications

Hyperpolarized Xenon for NMR and MRI Applications

Published on: September 6, 2012

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Related Experiment Videos

Last Updated: Jun 19, 2026

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Published on: August 17, 2017

Hyperpolarized Xenon for NMR and MRI Applications

Hyperpolarized Xenon for NMR and MRI Applications

Published on: September 6, 2012

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Main Results:

Demonstrated high stability and reproducibility in both constructed (87)Rb D(2) spectrometers.
Achieved excellent agreement between the two independent spectroscopic systems.
Reduced the uncertainty in determining the magnetic dipole (A) and electric quadrupole (B) hyperfine constants by a factor of 10.

Conclusions:

The developed spectrometers offer a robust platform for precise atomic measurements.
The significant reduction in uncertainty advances the field of atomic structure determination.
These findings have implications for improving atomic clocks and quantum sensing technologies.