caesium frequency

SI defining constant

Name	Symbol	Base units
caesium frequency	Δν_Cs	s^-1
The numerical value of the caesium frequency Δν_Cs, the frequency of radiation that is produced when an atom of caesium-133 in its unperturbed ground state undergoes a hyperfine transition, is defined to be exactly 9 192 631 770 when expressed in the unit hertz, or s^-1.
$\Delta \nu _{Cs} = 9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770 \mspace{6mu} \text{Hz}$

Frequency

The hyperfine transition frequency of the caesium-133 atom, Δν_Cs, forms the basis for the definition of the unit of frequency, the hertz.

The fixed numerical value of the caesium frequency, Δν_Cs, is defined exactly:

$\Delta \nu _{Cs} \mspace{4mu} = 9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770 \mspace{6mu} \text{Hz}$

Inverting this relation gives an exact expression for the hertz in terms of the caesium frequency, Δν_Cs :

$1 \mspace{4mu} \text{Hz} \mspace{6mu} = \dfrac{1}{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{6mu} 770} \mspace{6mu} \Delta \nu _{Cs}$

Time

The hyperfine transition frequency of the caesium-133 atom, Δν_Cs, forms the basis for the definition of the unit of time, the second.

The definition of the second implies the exact relation:

$\Delta \nu _{Cs} \mspace{4mu} = 9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770 \mspace{6mu} \text{s}^{-1}$

Inverting this relation gives an expression for the second in terms of the caesium frequency, Δν_Cs :

$1 \mspace{4mu} \text{s} \mspace{4mu} = 9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770 \mspace{6mu} \Delta {\nu _{Cs}}^{-1}$

Nature

Caesium-133 is the only stable isotope of caesium (element atomic number 55).

The unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, symbol Δν_Cs, has the character of an atomic parameter, which may be affected by the environment, such as electromagnetic fields. However, the underlying transition is well understood, stable and a good choice as a reference transition under practical considerations.

The choice of an atomic parameter like Δν_Cs does not disconnect definition and realisation in the same way that h, c, e, or k do, but specifies the reference.