Thecaesium standard is a primaryfrequency standard in which thephoton absorption by transitions between the twohyperfineground states ofcaesium-133atoms is used to control the output frequency. The first caesium clock was built byLouis Essen in 1955 at theNational Physical Laboratory in the UK[1] and promoted worldwide byGernot M. R. Winkler of theUnited States Naval Observatory.
Caesiumatomic clocks are one of the most accuratetime andfrequency standards, and serve as theprimary standard for the definition of thesecond in theInternational System of Units (SI), the modernmetric system. By definition,radiation produced by the transition between the two hyperfine ground states of caesium-133 (in the absence of external influences such as theEarth's magnetic field) has a frequency,ΔνCs, of exactly9192631770 Hz. That value was chosen so that thecaesium second equaled, to the limit of measuring ability in 1960 when it was adopted, the existing standardephemeris second based on theEarth's orbit around theSun.[2] 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 onlybase 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 themole and everynamed derived unit except thecoulomb,gray,sievert,radian, andsteradian have values that are implicitly at least partially defined by the properties of the caesium-133 hyperfine transition radiation. And of these, all but the mole, the coulomb, and thedimensionless radian and steradian are implicitly defined by the general properties ofelectromagnetic radiation.
The official definition of thesecond was first given by theBIPM at the 13thGeneral Conference on Weights and Measures in 1967 as: "The second is the duration of9192631770 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."[3]
The BIPM restated this definition in its 26th conference (2018), "The second is defined by taking the fixed numerical value of the caesium frequency ∆νCs, 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."[4]
The meaning of the preceding definition is as follows. The caesium atom has a ground state electron state withconfiguration [Xe] 6s1 and, consequently,atomic term symbol2S1/2. This means that there is one unpaired electron and the totalelectron 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 calledhyperfine interaction, 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 spinF equal toF = 7/2 + 1/2 = 4; the other sub-level corresponds to anti-parallel electron and nuclear spin (i.e., pointing in opposite directions), leading to a total spinF = 7/2 − 1/2 = 3. In the caesium atom it so happens that the sub-level lowest in energy is the one withF = 3, while theF = 4 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 theF = 3 sub-level to theF = 4 one. After some time the atom will re-emit the radiation and return to itsF = 3 ground state. From the definition of the second it follows that the radiation in question has a frequency of exactly9.19263177 GHz, corresponding to awavelength of about 3.26 cm and therefore belonging to themicrowave range.
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 meanradians per second. In contrast, the unit Hz should be interpreted ascycles 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).
Suppose the caesium standard has the parameters:
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:
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 thetropical year and before 1960 by the length of themean solar day[5]
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:
Between 1960 and 1983, the metre had been defined by the wavelength of a different transition frequency associated with thekrypton-86 atom. This had a much higher frequency and shorter wavelength than the caesium standard, falling inside thevisible spectrum. The first definition, used between 1889 and 1960, was by theinternational prototype meter.[6]
Following the2019 revision of the SI, electromagnetic radiation, in general, was explicitly defined to have the exact parameters:
The caesium-133 hyperfine transition radiation was explicitly defined to have frequency:
Though the above values forc andΔνCs were already obviously implicit in the definitions of the metre and second. Together they imply:
Notably, the wavelength has a fairly human-sized value of about 3.26 centimetres and the photon energy is surprisingly close to the average molecularkinetic energy perdegree of freedom perkelvin. From these it follows that:
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 theInternational Prototype of the Kilogram (IPK), a specific object stored at the headquarters of theInternational Bureau of Weights and Measures inParis, 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.[8]
From 1954 to 2019, the SI temperature scales were defined using thetriple point of water andabsolute zero.[9] The 2019 revision replaced these with an assigned value for theBoltzmann constant,k, of1.380649×10−23 J⁄K, implying:
The mole isan extremely large number of "elementary entities" (i.e.atoms,molecules,ions, etc). From 1969 to 2019, this number was 0.012 × the mass ratio between the IPK and acarbon 12 atom.[10] The 2019 revision simplified this by assigning the Avogadro constant the exact value6.02214076×1023 elementary entities per mole, thus, uniquely among the base units, the mole maintained its independence from the caesium standard:
Prior to the revision, the ampere was defined as the current needed toproduce a force between 2 parallel wires 1 m apart of 0.2μN per meter. The 2019 revision replaced this definition by givingthe charge on the electron,e, the exact value1.602176634×10−19 coulombs. Somewhat incongruously, the coulomb is still considered a derived unit and the ampere a base unit, rather than vice versa.[11] In any case, this convention entailed the following exact relationships between the SI electromagnetic units, elementary charge, and the caesium-133 hyperfine transition radiation:
From 1967 to 1979 the SI optical units, lumen, lux, and candela are defined using theincandescent glow ofplatinum at its melting point. After 1979, the candela was defined as theluminous intensity of amonochromaticvisible light source of frequency 540 THz (i.e6000/1.02140353 that of the caesium standard) andradiant intensity1/683 watts per steradian. This linked the definition of the candela to the caesium standard and, until 2019, to the IPK. Unlike the units relating tomass,energy,temperature,amount of substance, andelectromagnetism, the optical units werenot massively redefined in 2019, though they were indirectly affected since their values depend on that of the watt, and hence of the kilogram.[12] The frequency used to define the optical units has the parameters:
This implies:
The parameters of the caesium-133 hyperfine transition radiation expressed exactly in SI units are:
If the seven base units of the SI are expressed explicitly in terms of the SI defining constants, they are:
Ultimately, 6 of the 7 base units (all but the dimensionless mole) notably have values that depend on that ofΔνCs, which appears far more often than any of the other defining constants. However, the derived unit of one coulomb, which is an ampere-second, is a dimensionful unit defined purely in terms of the elementary charge and hence is independent ofΔνCs.
This article incorporatespublic domain material fromFederal Standard 1037C.General Services Administration. Archived fromthe original on 2022-01-22. (in support ofMIL-STD-188).