Von Klitzing's constant

Physical constant
Surname	Von Klitzing's constant
Formula symbol	${\displaystyle R_{\text{K}}}$
value
SI	2.581 280 745 ...e4th ${\displaystyle \textstyle \mathrm {\Omega } }$
Uncertainty  (rel.)	(exactly)
Relation to other constants
${\displaystyle R_{\text{K}}={\frac {h}{e^{2}}}}$ ${\displaystyle e}$- Elementary charge - Planck's quantum of action ${\displaystyle h}$
Sources and Notes
Source of the SI value: CODATA 2018 ( direct link )

The von Klitzing constant , also known as Klitzing constant, is a physical constant of the resistance dimension . As a quantum of the quantum Hall effect , it is named after its discoverer Klaus von Klitzing . ${\displaystyle R_{\mathrm {K} }}$

The Von Klitzing constant is related to Planck's quantum of action  and the elementary charge as follows: ${\displaystyle h}$  ${\displaystyle e}$

${\displaystyle R_{\text{K}}={\frac {h}{e^{2}}}}$.

The constants and in SI units are precisely defined. The value of the Von Klitzing constant is: ${\displaystyle h}$ ${\displaystyle e}$

${\displaystyle R_{\mathrm {K} }={\frac {6{,}626\,070\,15\cdot 10^{-34}\mathrm {J\cdot s} }{(1{,}602\,176\,634\cdot 10^{-19}\mathrm {C} )^{2}}}=25\ 812{,}807\ 45\ldots \ \Omega .}$

old value

Before the redefinition of the SI units in 2019, it had to be determined experimentally. The value was: ${\displaystyle R_{\text{K}}}$

${\displaystyle R_{\text{K}}=25\,812{,}807\,4555(59)\,\Omega }$

The numbers in brackets indicate the uncertainty in the last digits of the value; this uncertainty is given as the estimated standard deviation of the specified numerical value from the actual value. ${\displaystyle 5{,}9\cdot 10^{-6}\;\Omega }$

Since Von Klitzing's constant can be measured relatively easily, it has been proposed to use it as a standard for measurements of electrical resistance. For this purpose, the conventional ohm was defined in such a way that: ${\displaystyle \Omega _{90}}$

${\displaystyle R_{\text{K}}=25\,812{,}807\,\Omega _{90}}$.

With the redefinition of the SI units, the definition of the conventional ohm that had been in force since 1990 was abolished with effect from May 20, 2019.

Individual evidence

1. ↑ The value of the Von Klitzing constant is exact . However, the numerical value as the quotient of the other exact constants does not have a finite representation of the decimal places and must therefore be abbreviated with ...
2. ↑ CODATA Recommended Values. National Institute of Standards and Technology, accessed May 22, 2019 .  Value for ${\displaystyle R_{\text{K}}}$
3. ↑ CODATA Recommended Values. National Institute of Standards and Technology, accessed August 12, 2019 .  Value for ${\displaystyle R_{\text{K-90}}}$
4. ↑ 26th CGPM (2018) - Resolutions adopted / Résolutions adoptées. (PDF; 1.2 MB) Versailles 13–16 November 2018. In: bipm.org. Bureau International des Poids et Mesures, November 19, 2018, pp. 2–5 , accessed on April 28, 2019 (en / fr).