A new definition of mass using Planck constant

Tonight in a italian television news channel well known internationally I have heard that almost certainly the definition of mass that we currently know will be obtained by means of the constant Planck exploiting the silicium atoms. How will the Planck constant be used mathematically? I wanted to better understand the question, not clear to me, even with any mathematical steps just to understand how in the future will be given the definition of mass and its unit of measure the kilogram in the International System.

The new kilogram is being defined by defining Planck's constant $$h$$ to be exactly $$6.62607015\times 10^{-34}$$ joule-seconds.

This is similar to how the meter was previously defined by defining the speed of light $$c$$ to be exactly 299792458 meters per second.

Redefining the kilogram requires redefining other units that depend on the kilogram. So there are also new exact values for the element charge $$e$$, the Boltzmann constant $$k$$, and the Avogadro constant $$N_A$$.

All this is explained here: https://en.wikipedia.org/wiki/Proposed_redefinition_of_SI_base_units

• Unfortunately they did not fix that stupid situation of basic unit being multiple with decadic prefix. – mykhal Nov 16 '18 at 16:43
• In the meantime, as it is correct and in my opinion, the same as that which follows my life and my professional training, always vote in favour of whatever answer is given that is obviously correct. I follow the same practice in the TeX.SE website where I devote much more time. Can I ask for a courtesy? You could give me a concrete example of how the kilogram is used as a unit of measure by using your indication from your explanation from "Redefining" to "$N_A$". Could you better explain to me in your own words the intervention of Planck's constant for one kilogram, with mathematical passages? – Sebastiano Nov 16 '18 at 16:46
• @mykhal I have not understood your comment. – Sebastiano Nov 16 '18 at 16:47
• @Sebastiano I mean kilo- gram. – mykhal Nov 16 '18 at 16:49
• The details are complicated but explained here: en.m.wikipedia.org/wiki/Kibble_balance. Using a device called a Kibble balance, you can measure mass this way: $m=UI/gv$, where $U$ is a potential difference, $I$ is a current, $g$ is an acceleration, and $v$ is a speed. Measuring $g$ and $v$ involves only the existing definitions of the meter and the second. Measuring $U$ and $I$ involves the Josephson constant $2e/h$ and the von Kitzling constant $h/e^2$. Thus if one defines exact values for $h$ and $e$, one can use a Kibble balance to measure mass without already having a unit of mass. – G. Smith Nov 16 '18 at 17:56