Determination
| Method | Value of h (10−34 J·s) |
Relative uncertainty |
Ref. |
|---|---|---|---|
| Watt balance | 6.62606889(23) | 3.4×10−8 | |
| X-ray crystal density | 6.6260745(19) | 2.9×10−7 | |
| Josephson constant | 6.6260678(27) | 4.1×10−7 | |
| Magnetic resonance | 6.6260724(57) | 8.6×10−7 | |
| Faraday constant | 6.6260657(88) | 1.3×10−6 | |
| CODATA 2010 recommended value |
6.62606957(29) | 4.4×10−8 | |
| The nine recent determinations of the Planck constant cover five separate methods. Where there is more than one recent determination for a given method, the value of h given here is a weighted mean of the results, as calculated by CODATA. | |||
In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of KJ2RK and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.
There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being there is no indication which method is at fault.
The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.
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