[time-nuts] Rb resonance

Tom Van Baak tvb at leapsecond.com
Sat Sep 17 04:44:55 EDT 2005

> The second is defined in terms of the Cs133 resonance- hence there is 
> an integer number of Hz in the resonance frequency viz. 9192 631 770 
> Hz.

A definition doesn't imply it has to be an integer. An
inch, for example, is defined to be 25.4 mm.

The cesium 9192631770 value looks like an integer only
because when the atomic second was calibrated against
the astronomical second in the 1950's the measurements
were precise or accurate to only 9 or 10 digits.

The value was reported as 9 192 631 770 +- 20 Hz which
was the simple average of several measurements made
between 1954 and 1958. A scan of the raw data is at:


If you do the math you can see that the average of
...761, 767, 772, 780 is ...770, the value we still use

See also the original 1958 Markowitz/Essen paper under:

>  But what about the Rb resonance frequency? It is always quoted as 
> being an integer number of Hz as well- viz 6834 682 608 Hz.   Is there 
> some aspect of the physics of these transition frequencies that means 
> the Rb resonance has to be an integer number of Hz, based on the Cs133 
> definition?
> Or is the Rb resonance frequency, which is generally quoted as above, 
> actually rounded to be an integer number of Hz for convenience? 
> Perhaps a set of environmental conditions need to be specified as 
> well?
> Regards,
> Dave Brown, NZ

Yes, depending on where you see the value it will be
rounded. The most accurate measurement that I've
seen for the Rb resonance is 6 834 682 612.904324 Hz.
But it is common to see  6.8 GHz, 6 834 MHz, and
6 834 682 612 Hz as well. Not sure about the ...608
vs. ...612 thing.

For Hydrogen and Mercury frequencies see the last
paragraph of:

Note that due to a variety of factors atomic frequency
standards don't actually operate right at their magic
frequencies. Most Cs, for example, run a few Hz higher
and the correction is transparently applied internally in
a combination of hardware or firmware.


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