frequency standard
A frequency standard is a stable oscillator used for frequency calibration or reference. A frequency standard generates a fundamental frequency with a high degree of accuracy and precision. Harmonics of this fundamental frequency are used to pro ...
hyperfine
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the ...
caesium-133
Caesium (55Cs) has 40 known isotopes, making it, along with barium and mercury, one of the elements with the most isotopes. The atomic masses of these isotopes range from 112 to 151. Only one isotope, 133Cs, is stable. The longest-lived radioisot ...
atoms is used to control the output frequency. The first caesium clock was built by
Louis Essen
Louis Essen FRS O.B.E. (6 September 1908 – 24 August 1997) was an English physicist whose most notable achievements were in the precise measurement of time and the determination of the speed of light. He was a critic of Albert Einstein' ...
Gernot M. R. Winkler
Gernot Maria Rudolph Winkler (October 17, 1922 – April 30, 2016) was responsible for the Time Service Department of the United States Naval Observatory (USNO) from 1966 to 1996.
Winkler oversaw the introduction of caesium beam-based Coordinat ...
atomic clock
An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...
s are one of the most accurate time and frequency standards, and serve as the
primary standard A primary standard in metrology is a standard that is sufficiently accurate such that it is not calibrated by or subordinate to other standards. Primary standards are defined via other quantities like length, mass and time. Primary standards are u ...
for the definition of the second in the International System of Units (SI) (the modern form of the metric system). By definition, radiation produced by the transition between the two hyperfine ground states of caesium (in the absence of external influences such as the Earth's magnetic field) has a frequency, , of exactly . That value was chosen so that the caesium second equalled, to the limit of human measuring ability in 1960 when it was adopted, the existing standard ephemeris second based on the Earth's orbit around the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
. Because no other measurement involving time had been as precise, the effect of the change was less than the experimental uncertainty of all existing measurements.
While the second is the only base unit to be explicitly defined in terms of the caesium standard, the majority of SI units have definitions that mention either the second, or other units defined using the second. Consequently, every base unit except the mole and every named derived unit except the coulomb, ohm, siemens, weber, gray, sievert, radian, and steradian have values that are implicitly defined by the properties of the caesium-133 hyperfine transition radiation. And of these, all but the mole, the coulomb, and the dimensionless radian and steradian are implicitly defined by the general properties of electromagnetic radiation.
Technical details
The official definition of the second was first given by the
BIPM
The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
at the 13th General Conference on Weights and Measures in 1967 as: "''The second is the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.''" At its 1997 meeting the BIPM added to the previous definition the following specification: "''This definition refers to a caesium atom at rest at a temperature of 0 K.''"
The BIPM restated this definition in its 26th conference (2018), "''The second is defined by taking the fixed numerical value of the caesium frequency ∆Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s–1.''"
The meaning of the preceding definition is as follows. The caesium atom has a ground state electron state with
configuration
Configuration or configurations may refer to:
Computing
* Computer configuration or system configuration
* Configuration file, a software file used to configure the initial settings for a computer program
* Configurator, also known as choice board ...
e6s1 and, consequently, atomic term symbol2S1/2. This means that there is one unpaired electron and the total electron spin of the atom is 1/2. Moreover, the nucleus of caesium-133 has a nuclear spin equal to 7/2. The simultaneous presence of electron spin and nuclear spin leads, by a mechanism called
hyperfine interaction
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the ...
, to a (small) splitting of all energy levels into two sub-levels. One of the sub-levels corresponds to the electron and nuclear spin being parallel (i.e., pointing in the same direction), leading to a total spin ''F'' equal to ; the other sub-level corresponds to anti-parallel electron and nuclear spin (i.e., pointing in opposite directions), leading to a total spin . In the caesium atom it so happens that the sub-level lowest in energy is the one with , while the sub-level lies energetically slightly above. When the atom is irradiated with electromagnetic radiation having an energy corresponding to the energetic difference between the two sub-levels the radiation is absorbed and the atom is excited, going from the sub-level to the one. After a small fraction of a second the atom will re-emit the radiation and return to its ground state. From the definition of the second it follows that the radiation in question has a frequency of exactly , corresponding to a wavelength of about 3.26 cm and therefore belonging to the
microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency rang ...
range.
This particular cesium resonance was agreed upon under la Convention du Mètre and remains to the present time as the official definition of the second for the world community.
Note that a common confusion involves the conversion from angular frequency () to frequency (), or vice versa. Angular frequencies are conventionally given as s–1 in scientific literature, but here the units implicitly mean ''radians'' per second. In contrast, the unit Hz should be interpreted as ''cycles'' per second. The conversion formula is , which implies that 1 Hz corresponds to an angular frequency of approximately 6.28 radians per second (or 6.28 s–1 where radians is omitted for brevity by convention).
Parameters and significance in the second and other SI units
The first set of units defined using the caesium standard were those relating to time, with the second being defined in 1967 as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom" meaning that:
* 1 second, s, = 9,192,631,770
* 1 hertz, Hz, = 1/s =
* 1
becquerel
The becquerel (; symbol: Bq) is the unit of radioactivity in the International System of Units (SI). One becquerel is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. For applications relatin ...
, Bq, = 1 nuclear decay/s = nuclear decays/
This also linked the definitions of the derived units relating to force and energy (see below) and of the ampere, whose definition at the time made reference to the newton, to the caesium standard. Before 1967 the SI units of time and frequency were defined using the
tropical year
A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time fro ...
In 1983, the meter was, indirectly, defined in terms of the caesium standard with the formal definition "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This implied:
* 1 metre, m, = = ''c'' =
* 1 radian, rad, = 1 m/m = / = 1 (dimensionless unit of angle)
* 1 steradian, sr, = 1 m2/m2 = 2/2 = 1 (dimensionless unit of solid angle)
Between 1960 and 1983, the metre had been defined by the wavelength of a different transition frequency associated with the krypton 86 atom. This had a much higher frequency and shorter wavelength than the caesium standard, falling inside the visible spectrum. And between 1889 and 1960 by the international prototype meter.
Mass, energy, and force
Following the
2019 redefinition of the SI base units
In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram.
Effective 20 May 2019, the 144th ...
, electromagnetic radiation, in general, was explicitly defined to have the exact parameters:
* ''c'' = 299,792,458 m/s
* ''h'' = J s
And the caesium 133 hyperfine transition radiation was explicitly defined to have frequency:
* = 9,192,631,770 Hz
Though the above values for ''c'' and were already obviously implicit in the definitions of the metre and second. Together they imply:
* = =
* = ''c'' = m
* = ''h'' = 9,192,631,770 Hz × J s = J
* = = = kg
Notably, the wavelength has a fairly human-sized value of about 3.26 centimetres and the photon energy is surprisingly close to the average molecular kinetic energy per
degree of freedom
Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...
per kelvin. From these it follows that:
* 1 kilogram, kg, =
* 1 joule, J, =
* 1 watt, W, = 1 J/s =
* 1 newton, N, = 1 J/m = /
* 1
pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, Frenc ...
, Pa, = 1 N/m2 = /3
* 1
gray
Grey (more common in British English) or gray (more common in American English) is an intermediate color between black and white. It is a neutral or achromatic color, meaning literally that it is "without color", because it can be composed ...
equivalent
Equivalence or Equivalent may refer to:
Arts and entertainment
*Album-equivalent unit, a measurement unit in the music industry
*Equivalence class (music)
*''Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre
*'' Equival ...
to 1 gray of
gamma rays
A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically sh ...
Prior to the revision, between 1889 and 2019, the family of metric (and later SI) units relating to mass, force, and energy were somewhat notoriously defined by the mass of the
International Prototype of the Kilogram
The International Prototype of the Kilogram (referred to by metrologists as the IPK or Le Grand K; sometimes called the '' ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in English) is an object that was used t ...
(IPK), a specific object stored at the headquarters of the
International Bureau of Weights and Measures
The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
in Paris, meaning that any change to the mass of that object would have resulted in a change to the size of the kilogram and of the many other units whose value at the time depended on that of the kilogram.
Temperature
From 1954 to 2019, the SI temperature scales were defined using the
triple point
In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.. It is that temperature and pressure at which the ...
of water and
absolute zero
Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibratio ...
. The 2019 revision replaced these with an assigned value for the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
, ''k'', of J/K, implying:
* 1 kelvin, K, = J/2 per degree of freedom = per degree of freedom = per degree of freedom
* Temperature in degrees
Celsius
The degree Celsius is the unit of temperature on the Celsius scale (originally known as the centigrade scale outside Sweden), one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The d ...
atoms
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, and ...
,
molecules
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
, ions, etc). From 1969 to 2019, this number was 0.012 × the mass ratio between the IPK and a carbon 12 atom. The 2019 revision simplified this by assigning the Avogadro constant the exact value elementary entities per mole, thus, uniquely among the base units, the mole maintained its independence from the caesium standard:
* 1
mole
Mole (or Molé) may refer to:
Animals
* Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America
* Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
, mol, = elementary entities
* 1
katal
The katal (symbol: kat) is the unit of catalytic activity in the International System of Units (SI) used for quantifying the catalytic activity of enzymes (that is, measuring the enzymatic activity level in enzyme catalysis) and other catalyst ...
, kat, = 1 mol/s = elementary entities/
Electromagnetic units
Prior to the revision, the ampere was defined as the current needed to produce a force between 2 parallel wires 1 m apart of 0.2 μN per meter. The 2019 revision replaced this definition by giving the charge on the electron, ''e'', the exact value coulombs. Somewhat incongruously, the coulomb is still considered a derived unit and the amp a base unit, rather than vice versa. In any case, this convention entailed the following exact relationships between the SI electromagnetic units, electron, and the caesium-133 hyperfine transition radiation:
* 1 coulomb, C, = ''e''
* 1
ampere
The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
, or amp, A, = 1 C/s = ''e''
* 1 volt, V, = 1 J/C = /''e''
* 1 farad, F, = 1 C/V = ''e''2/
* 1
ohm
Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm.
Ohm or OHM may also refer to:
People
* Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm''
* Germán Ohm (born 1936), Mexican boxer
* Jörg Ohm (bor ...
weber
Weber (, or ; German: ) is a surname of German origin, derived from the noun meaning " weaver". In some cases, following migration to English-speaking countries, it has been anglicised to the English surname 'Webber' or even 'Weaver'.
Notable pe ...
From 1967 to 1979 the SI optical units, lumen, lux, and candela are defined using the
Incandescent
Incandescence is the emission of electromagnetic radiation (including visible light) from a hot body as a result of its high temperature. The term derives from the Latin verb ''incandescere,'' to glow white. A common use of incandescence i ...
glow of
platinum
Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver".
Platin ...
at its melting point. After 1979, the candela was defined as the luminous intensity of a monochromaticvisible light source of frequency 540 Thz (i.e that of the caesium standard) and radiant intensity watts per steradian. This linked the definition of the candela to the caesium standard and, until 2019, to the IPK. Unlike the units relating to mass, energy, temperature,
amount of substance
In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
, and
electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
, the optical units were ''not'' massively redefined in 2019, though they were indirectly affected since their values depend on that of the watt, and hence of the kilogram. The frequency used to define the optical units has the parameters:
* Frequency: 540 THz
* Time period: fs
* Wavelength:
μm
The micrometre ( international spelling as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer ( American spelling), also commonly known as a micron, is a unit of length in the International System of Uni ...
Luminous energy
In photometry, luminous energy is the perceived energy of light. This is sometimes called the quantity of light.lumen, lm, =
* 1
candela
The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to ...
, cd, = 1 lm/sr = /sr
* 1
Lux
The lux (symbol: lx) is the unit of illuminance, or luminous flux per unit area, in the International System of Units (SI). It is equal to one lumen per square metre. In photometry, this is used as a measure of the intensity, as perceived by ...
, lx, = 1 lm/m2 = /2
Summary
The parameters of the caesium 133 hyperfine transition radiation expressed exactly in SI units are:
* Frequency = 9,192,631,770 Hz
* Time period =
* Wavelength = m
* Photon energy = J
* Photon mass equivalent = kg
If the 7 base units of the SI are expressed explicitly in terms of the SI defining constants, they are:
* 1 second =
* 1 metre = ''c''/
* 1 kilogram = ''h'' /''c''2
* 1 ampere = ''e''
* 1 kelvin = ''h'' /''k''
* 1 mole = elementary entities
* 1 candela = ''h'' 2 ''K''CD/sr
With 6 of the 7 base units notably having values that depend on that of . And appearing far more often than any of the other defining constants.
See also
*
Rubidium standard
A rubidium standard or rubidium atomic clock is a frequency standard in which a specified hyperfine transition of electrons in rubidium-87 atoms is used to control the output frequency.
Synopsis
The Rb standard is the most inexpensive, compact, ...