Editing Caesium standard (section)

== Technical details ==
The official definition of the [[second]] was first given by the [[International Bureau of Weights and Measures|BIPM]] at the 13th [[General Conference on Weights and Measures]] in 1967 as: "''The second is the duration of {{val|9192631770}} 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&nbsp;K.''"<ref>{{cite web |title=Comité international des poids et mesures (CIPM): Proceedings of the Sessions of the 86th Meeting |url=https://www.bipm.org/utils/common/pdf/CIPM-PV-OCR/CIPM1997.pdf |publisher=Bureau International des Poids et Mesures |location=Paris |pages=229 |language=FR, EN |date=23–25 Sep 1997 |access-date=30 December 2019 |archive-date=4 December 2020 |archive-url=https://web.archive.org/web/20201204121811/https://www.bipm.org/utils/common/pdf/CIPM-PV-OCR/CIPM1997.pdf |url-status=dead }}</ref>

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<sup>−1</sup>.''"<ref>{{cite web |title=Resolution 1 of the 26th CGPM |url=https://www.bipm.org/en/CGPM/db/26/1/ |publisher=Bureau International des Poids et Mesures |location=Paris |pages=472 of the official French publication |language=FR,EN |date=2018 |access-date=2019-12-29 |archive-date=2021-02-04 |archive-url=https://web.archive.org/web/20210204120336/https://www.bipm.org/en/CGPM/db/26/1/ |url-status=dead }}</ref>

The meaning of the preceding definition is as follows. The caesium atom has a ground state electron state with [[Electron configuration|configuration]] [Xe] 6s<sup>1</sup> and, consequently, [[Term symbol|atomic term symbol]] <sup>2</sup>S<sub>1/2</sub>. This means that there is one unpaired electron and the total [[Spin (physics)|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 structure|hyperfine 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 spin ''F'' equal to {{nowrap|1=''F'' = 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 spin {{nowrap|1=''F'' = 7/2 − 1/2 = 3}}. In the caesium atom it so happens that the sub-level lowest in energy is the one with {{nowrap|1=''F'' = 3}}, while the {{nowrap|1=''F'' = 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 the {{nowrap|1=''F'' = 3}} sub-level to the {{nowrap|1=''F'' = 4}} one. After some time the atom will re-emit the radiation and return to its {{nowrap|1=''F'' = 3}} ground state. From the definition of the second it follows that the radiation in question has a frequency of exactly {{val|9.19263177|u=GHz}}, corresponding to a [[Electromagnetic spectrum|wavelength]] of about 3.26&nbsp;cm and therefore belonging to the [[microwave]] range.

Note that a common confusion involves the conversion from angular frequency (<math>\omega</math>) to frequency (<math>f</math>), or vice versa. Angular frequencies are conventionally given as s<sup>−1</sup> 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 <math>\omega = 2\pi f</math>, which implies that 1 Hz corresponds to an angular frequency of approximately 6.28 radians per second (or 6.28 s<sup>−1</sup> where radians is omitted for brevity by convention).