Editing Caesium standard (section)

=== Mass, energy, and force ===

Following the [[2019 revision of the SI]], electromagnetic radiation, in general, was explicitly defined to have the exact parameters:
* ''c'' = 299,792,458 m/s
* ''h'' = {{val|6.62607015|e=-34}} J s

The caesium-133 hyperfine transition radiation was explicitly defined to have frequency:
* {{math|Δ''ν''<sub>Cs</sub>}} = 9,192,631,770 Hz<ref>{{Cite web|url=https://www.bipm.org/en/committees/cg/cgpm/26-2018/resolution-1|title = Resolution 1 (2018) - BIPM}}</ref>

Though the above values for ''c'' and {{math|Δ''ν''<sub>Cs</sub>}} were already obviously implicit in the definitions of the metre and second. Together they imply:
* {{math|Δ''t''<sub>Cs</sub>}} = {{sfrac|1|{{math|Δ''ν''<sub>Cs</sub>}}}} = {{sfrac|s|9,192,631,770}}
* {{math|Δ''λ''<sub>Cs</sub>}} = ''c'' {{math|Δ''t''<sub>Cs</sub>}} = {{sfrac|299,792,458|9,192,631,770}} m
* {{math|Δ''E''<sub>Cs</sub>}} = ''h'' {{math|Δ''ν''<sub>Cs</sub>}} = 9,192,631,770 Hz × {{val|6.62607015|e=-34}} J s = {{val|6.09110229711386655|e=-24}} J
* {{math|Δ''M''<sub>Cs</sub>}} = {{sfrac|{{math|Δ''E''<sub>Cs</sub>}}|''c''<sup>2</sup>}} = {{sfrac|{{val|6.09110229711386655|e=-24}} J|89,875,517,873,681,764 m<sup>2</sup>/s<sup>2</sup>}} = {{sfrac|{{val|6.09110229711386655}}|{{val|8.9875517873681764|e=40}}}} 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 [[Degrees of freedom (physics and chemistry)|degree of freedom]] per [[kelvin]]. From these it follows that:
* 1 [[kilogram]], kg, = {{sfrac|{{val|8.9875517873681764|e=40}}|{{val|6.09110229711386655}}}} {{math|Δ''M''<sub>Cs</sub>}}
* 1 [[joule]], J, = {{sfrac|{{val|e=24}}|{{val|6.09110229711386655}}}} {{math|Δ''E''<sub>Cs</sub>}}
* 1 [[watt]], W, = 1 J/s = {{sfrac|{{val|e=14}}|{{val|5.59932604907689089550702935}}}} {{math|Δ''E''<sub>Cs</sub>}} {{math|Δ''ν''<sub>Cs</sub>}}
* 1 [[Newton (unit)|newton]], N, = 1 J/m = {{sfrac|{{val|2.99792458|e=22}}|{{val|5.59932604907689089550702935}}}} {{math|Δ''E''<sub>Cs</sub>}}/{{math|Δ''λ''<sub>Cs</sub>}}
* 1 [[Pascal (unit)|pascal]], Pa, = 1 N/m<sup>2</sup> = {{sfrac|{{val|2.6944002417373989539335912|e=19}}|{{val|4.73168129737820913189287698892486811451620615}}}} {{math|Δ''E''<sub>Cs</sub>}}/{{math|Δ''λ''<sub>Cs</sub>}}<sup>3</sup>
* 1 [[Gray (unit)|gray]], Gy, = 1 J/kg = {{sfrac|1|89,875,517,873,681,764}} {{math|Δ''E''<sub>Cs</sub>}}/{{math|Δ''M''<sub>Cs</sub>}} = {{sfrac|''c''<sup>2</sup>|89,875,517,873,681,764}}
* 1 [[sievert]], Sv, = the [[ionizing radiation]] dose [[Equivalent dose|equivalent]] to 1 gray of [[gamma rays]]

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]] (IPK), a specific object stored at the headquarters of the [[International Bureau of Weights and Measures]] 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.<ref>{{Cite web|url=https://www.bipm.org/en/history-si/kilogram|title = Kilogram - BIPM}}</ref>