The NIST Reference on Constants, Units and Uncertainty

Fundamental Physical Constants


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Introduction to the constants for nonexperts

Introduction 1900 - 1920 1920 - 1940 1940 - 1960 Current (index)

The great progress made in determining the numerical values of the fundamental constants after World War II is the direct result of the advances made in the general fields of electronics, microwaves, and other technologies during the war. These advances have not only resulted in new and improved measurements of some of the constants listed earlier (for example, a 1957 velocity of light determination using a microwave interferometer) but for the first time permitted the direct measurement of a whole new group of constants and related quantities. The more important of these new measurements are as follows, the first two of which are concerned with the proton, an atomic particle having a mass approximately 1836 times that of an electron and a charge identical to the electron charge, only positive:

Gyromagnetic ratio of the proton

    This quantity, symbolized by the Greek letter gamma followed by a subscript p, is a measure of how fast the axis of the proton's intrinsic rotational motion, or spin, precesses (swings) in a magnetic field much like how a child's top wobbles as it spins on the floor. It may be determined by first establishing a known magnetic field that has been produced by the passage of a known electric current through a precision coil, or solenoid, of known dimensions and then measuring by means of standard electronic techniques the precession frequency of the protons in a water sample within the solenoid. This procedure is the low-field method, in which the accurately determined magnetic field is only about 20 times the Earth's magnetic field. In the high-field method, the magnetic field, established by an electromagnet, may be 10 000 times larger. For this case, the field is determined by measuring the force it exerts on a small coil of known dimensions carrying a known current; this apparatus is often called a Cotton balance. The gyromagnetic ratio of the proton was first determined to high accuracy by the high-field method in 1950 and by the low-field method in 1957.

Magnetic moment of the proton

    The magnetic moment of the proton in nuclear magnetons (µp/µN, µ is the Greek letter mu), is the ratio of the above mentioned spin axis precession frequency of a proton in a magnetic field to the frequency of the proton's orbital, or circular, motion in the same field, called the cyclotron frequency. The first measurement of this ratio was reported in 1949 by physicists in the United States, John A. Hipple and his associates, using a small, metal, boxlike device called an omegatron. In this method, an adjustable radio- frequency electric field is applied to the omegatron at right angles to the direction of the magnetic field. When the frequency of this electric field is properly adjusted, protons in the omegatron are accelerated by it and spiral outward until they hit an internal collector and are detected. The frequency of the proton's orbital motion can then be determined from the adjusted frequency of the electric field.

Fine structure of atomic hydrogen

    The term fine structure refers to the differences between certain states of energy or energy levels in atoms. The fine structure of atomic hydrogen was first measured with high accuracy by a United States physicist, Willis E. Lamb, Jr., and coworkers and reported in a series of classic papers over the period 1950 to 1953. In these experiments, changes in the energy state of particular atoms or, equivalently, transitions between energy levels in the atoms themselves were induced by irradiating a beam of the atoms with microwaves of a properly adjusted and known frequency as the beam was passed through a known magnetic field. The energy differences, or fine structure could then be accurately calculated from the field and frequency.

Free electron g factor

    Because the electron has an electric charge and an intrinsic rotational motion, or spin, it behaves in some respects like a small bar magnet; that is, it is said to have a magnetic moment. Because the electron also has mass, it behaves in some respects like a spinning top; that is, it is said to have spin angular momentum. The g factor of the electron is defined as the ratio of its magnetic moment to its spin angular momentum. This factor is nominally 2 and was first measured with high accuracy during the period from 1961 to 1963. Using electric and magnetic fields, electrons were trapped with spins prealigned in a particular direction for a known length of time. The g factor was then obtained from the change in spin direction during the trapping period and the magnitude of the trapping magnetic field. Recent improvements in this basic method of measuring the g factor reduced the original 0.027 parts per million uncertainty obtained earlier to 0.003 parts per million.

Ground state hyperfine splitting (hfs) in atomic hydrogen

    The ground state, or lowest energy state, hyperfine splitting in hydrogen is basically equal to the energy difference between a hydrogen atom in which the spin of the orbital electron is in the same direction as that of the spin of the central proton and a hydrogen atom in which the spins of the electron and proton are in opposite directions. Polykarp Kusch, a physicist working in the United States, reported the first high-accuracy measurement of this quantity in 1955, using a microwave-excitation method not too unlike that used for fine-structure measurements.

    A much more accurate value was obtained in 1963 by a U.S. physicist, Norman F. Ramsey, and coworkers using the so-called hydrogen maser, which is a type of microwave amplifier. In this device, excited hydrogen atoms are focussed by a magnetic field onto an aperture in a Teflon-coated quartz bulb that is located in a radio-frequency-resonant metallic cavity. When the cavity frequency is tuned to the frequency corresponding to the hyperfine-splitting energy difference, maser-like oscillations are produced. The measurable oscillation frequency then equals the hyperfine splitting.


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Reproduced with permission from Encyclopaedia Britannica, 15th edition. © 1974 Encyclopaedia Britannica, Inc.