New Kilogram!

What news! There’s a new kilogram on the block! Le Grande K is being replaced by defining Planck’s constant to \(\Large{h=6.626\ 070\ 15\times10^{-34}{\rm J\ s}}\). The kilogram is hiding in the “J”, the joule, which is a compound unit \(\Large{{\rm kg}\frac{{\rm m}^2}{{\rm s}^2}}\). It isn’t official until May 2019, but it nails down another universal constant!

It’s perhaps less exciting, but just as important, that other constants are also being defined. The highlighted rows are the new definitions:

ConstantValue
\(\Large{\Delta v_{\rm Cs}}\) \(\Large{9\ 192\ 631\ 770{\rm Hz}}\)
\(\Large{c}\) \(\Large{299\ 792\ 458\frac{\rm m}{\rm s}}\)
\(\Large{h}\) \(\Large{6.626\ 070\ 15\times10^{-34}{\rm J\ s}}\)
\(\Large{e}\) \(\Large{1.602\ 176\ 634\times10^{-19}{\rm C}}\)
\(\Large{k}\) \(\Large{1.380\ 649\times10^{-23}\frac{\rm J}{\rm K}}\)
\(\Large{N_A}\) \(\Large{6.022\ 140\ 76\times10^{23}\frac{1}{\rm mol}}\)
\(\Large{K_{cd}}\) \(\Large{683\frac{\rm lm}{\rm W}}\)

This allows the definition of the seven SI units to universal constants.

Unit Definition
second (s) \(\Large{\frac{1}{\Delta\nu_{Cs}}}\)
meter (m) \(\Large{\frac{c}{\Delta\nu_{Cs}}}\)
kilogram (kg) \(\Large{\frac{c^2}{h\cdot\Delta\nu_{Cs}}}\)
ampere (A) \(\Large{\frac{1}{e\cdot\Delta\nu_{Cs}}}\)
kelvin (K) \(\Large{\frac{k}{h\Delta\nu_{Cs}}}\)
mole (mol) \(\Large{N_A}\)
candela (cd) \(\Large{\frac{1}{h\cdot\Delta\nu_{Cs}^2\cdot K_{cd}}}\)

The compound units used in the definitions of the constants are a shorthand.

Another aspect that is not getting much press is the downside of defining the kilogram and Avogadro’s number: 1 mole of 12C no longer has an exact mass of 0.012 kg. Now the mass of 12C is \(\Large{0.0120000000(45)\frac{kg}{mol}}\). Perhaps in the future these definitions can be reintegrated. Technically, they are still related by \(\Large{N_A=\frac{\alpha^2M({\rm e}^-)c}{2R_\infty h}}\), but we aren’t exactly certain about the values of \(\Large{\alpha}\), \(\Large{M({\rm e}}\), or \(\Large{R_\infty}\), so there’s still work to be done! Avogadro’s number may not move, but we may figure out these guys yet!

While these changes are official, they don’t become “the definition” until 20 May 2019, so you’ve still got some time to adjust your voltmeter by 0.00001% or so.

A tous les temps, à tous les peuples.

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