B So what is the new definition of the kilogram?

[GTrax]

So there is now one physical reference that underlies all our standards of measurement: the Cs-133 ground-state hyperfine splitting.

Indeed! You have it all. It seems the clock-makers have finally won!
However much we (rightly) desire to to lock our measurements to quantities we perceive to be constant, we always need some physical phenomenon with such unvarying properties that we can use it as a standard. Le Grand K and it's copies were pretty good for most practical needs, and may even remain so into the future, but with the advantage that we now have a way to calibrate them against something better.

Getting to a metre via the agreed (constant) speed of light, and a time standard, requires the second be set to an extraordinary degree of precision, and the NIST folk have managed just that! Cs-133 appears to vary so little we may consider it to be a constant good enough to use to define the second.

As I understand it, Planck's constant is now held to a fixed value, and we use a Kibble balance, or any other future apparatus, to determine an offered mass to be calibrated. The other route to a kilogram is via Avogadro's number, and our ability to create a sphere of purest silicon-28 with something close to the correct number of Si atoms in it. The two routes can be used each to check the other into the future, perhaps with ever better apparatus.

Measuring the Si-28 sphere is determining distance, so leads back to Cs-133 as the constant-setter.

 

[GuyBarry]

I rather like this handy little diagram:

https://en.wikipedia.org/wiki/2019_...#/media/File:Unit_relations_in_the_new_SI.svg

As I understand it, Planck's constant is now held to a fixed value, and we use a Kibble balance, or any other future apparatus, to determine an offered mass to be calibrated. The other route to a kilogram is via Avogadro's number

I don't think Avogadro's number will have any relation to the definition of the kilogram. Avogadro's number will be used to define the mole, and the connection between the mole and the kilogram will be broken.

Under the new definition the mole isn't really a "unit" as far as I can see - it's just a scale factor, 6.022 140 76×10²³. That number has been chosen because it makes the definition of the mole as close as possible to the old one based on 0.012kg of carbon-12, but really any scale factor could have been chosen and the definition would still have been consistent. Avogadro's number isn't really a genuine physical constant like the other ones whose value is being fixed.

 

[lpetrich]

That scale factor, Avogadro's number, is the number of atomic mass units in the gram, and the amu or dalton has gone through various definitions that I'd posted on earlier.

 

[GuyBarry]

That scale factor, Avogadro's number, is the number of atomic mass units in the gram,

Well it was, but it won't be any more. It will be a number chosen to be as close as possible to the number of atomic mass units in the gram, but it won't actually be the number of atomic mass units in the gram. It will simply be a number laid down in the definitions of the SI, with no actual connection to the atomic mass unit or to the gram.

Here's the new definition:

The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76×10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, N_A, when expressed in the unit mol⁻¹ and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

And that's all it says. The new definition of the mole is completely independent of all the other definitions of the SI.

 

[lpetrich]

That scale factor, Avogadro's number, is the number of atomic mass units in the gram,

Well it was, but it won't be any more. It will be a number chosen to be as close as possible to the number of atomic mass units in the gram, but it won't actually be the number of atomic mass units in the gram. It will simply be a number laid down in the definitions of the SI, with no actual connection to the atomic mass unit or to the gram.

Why do you think that that is the case? The atomic mass unit was recently defined as 1/12 of the mass of one carbon-12 atom, unbound and in its ground state. Avogadro's number is the number of amu's in a gram. Since that number is now fixed, the amu will no longer be 1/12 the mass of a carbon-12 atom, but 1/(A's N) grams.

 

[GuyBarry]

Why do you think that that is the case? The atomic mass unit was recently defined as 1/12 of the mass of one carbon-12 atom, unbound and in its ground state. Avogadro's number is the number of amu's in a gram. Since that number is now fixed, the amu will no longer be 1/12 the mass of a carbon-12 atom, but 1/(A's N) grams.

Is the definition of the amu going to change as the result of the SI redefinitions then? I understood that the amu was a non-SI unit accepted for use with the SI, and that its value was obtained experimentally. That's certainly what it says in the BIPM's https://www.bipm.org/utils/en/pdf/si-revised-brochure/Draft-SI-Brochure-2018.pdf:

The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 of the mass of a free carbon 12 atom, at rest and in its ground state

I'm not aware that the definition of the amu is due to be changed when the new SI definitions are adopted.

 

[GTrax]

As I understand it, the Plank constant was chosen as a current definition, but other natural constants can be used to provide a check, and there is definitely effort at NIST to define NA with greater precision. Avoadro's number depends on the mass of a substance, so it is easy to see why a very well-defined Avogadro number can provide a new kilogram definition to compete with, and to augment the Planck definition.
The present effort is based on spheres of a known number of atoms of Silicon-28

Instead of fixing Planck's constant, we could have fixed NA, and defined the kilogram as 1000*NA/12 atoms of carbon-12. Now that we have decided on Planck's constant definition, we still have to now accurately find a new NA in agreement.

Regarding the spheres, it seems they now have it to less than 10 parts per billion if the work in several countries is combined!

I don't know if making spheres of pure enough Si-28 is any more convenient and less costly than a Kibble balance, but clearly it is not like keeping a (changing) platinum-iridium cylinder in Paris, and similarly divergent copies at various other places. Anyone could polish up such a sphere to the required dimension, though admittedly first having to find/make some pure enough silicon. Though made using standard optical polishing techniques, the radius accuracy would likely be something less than about 50 atoms, but I am still looking around for some verification of just how well these have to be made.

I was distracted by the beauty of thing, but I came across the information about the efforts by Bureau International Des Poids et Mesures and NIST at these links..
https://www.bipm.org/en/bipm/mass/avogadro/
https://www.nist.gov/si-redefinition/kilogram-silicon-spheres-and-international-avogadro-project.

One part of the rationale mentions that NA can also be used to obtain Planck’s constant using the well-known values of other constants. I do not yet know which constants these are, nor how the relationships work.

We start with something we hold to be "constant", and find the factor agreed to get close enough, as best we can, to the le Grand K as was widely used, and then stop messing with it, and let the new Planck definition be the definer.

Other quantities may need some consequential revision to be "in agreement". Either way, the generation of stable accurate standards, completely in sync with the Planck definition, and possibly less costly, would seem to be a possible positive benefit.

 

[f95toli]

I don't know if making spheres of pure enough Si-28 is any more convenient and less costly than a Kibble balance,

.

Don't underestimate how difficult it is to make Si-28 with the required purity. The "Avogadro Silicon" has uses outside of the redefinition of the SI and small pieces are used in other research project (in some cases literally off-cuts from the sphere) but it is still extremely rare and expensive; it is certainly not something you can buy commercially,.
The project to create this was -if I understand correctly- originally a cost-is-no-object effort to keep a number of very talented scientists from the former Soviet Union busy. That is, the point of the project was to make sure that people/facilities who were very good a purifying isotopes had something meaningful to do, and to make sure they did not take up an offer to go off and purify isotopes somewhere else...say plutonium in the ME.

The point is that the Kibble balance is not THAT complicated. Moreover, simpler versions are under development which will be good enough for most commercial calibration labs to use. That is, these labs will not need to send their standards to NMI once a year to be calibrated.

Note that one of the main point of the new SI is that it will allow for end-users to have their own primary standards that will never need to be calibrated. The accuracy of these will of course be lower than what will be used at NMIs, but most users do not need that accuracy anyway.
Moreover, the fact that you don't need a calibration chain almost automatically gives you a gain of 10-1000 in accuracy depending on the unit (you loose about one order of magnitude per step in the chain).

 

[Dale]

there is definitely effort at NIST to define NA with greater precision.

Not any more. Avogadro’s number is now exact.

Instead of fixing Planck's constant, we could have fixed NA, and defined the kilogram as 1000*NA/12 atoms of carbon-12. Now that we have decided on Planck's constant definition, we still have to now accurately find a new NA in agreement.

This is not correct. Both numbers are now fixed.

 

[GuyBarry]

Indeed they are. And the reason why it's been possible to fix both numbers is that the Avogadro constant is unconnected with the definition of the kilogram. It is the number of elementary entities in one mole. Fixing both numbers required the breaking of the connection between the kilogram and the mole.

The molar mass constant, which until now has been defined at exactly 1 g/mol, will now be determined experimentally.

 

[gmax137]

Avogadro’s number is now exact.

is that the Avogadro constant is unconnected with the definition of the kilogram

Right, like "a dozen" means twelve of anything. Twelve apples, twelve dwarves, twelve eggs. Avogadro's number is a super-jumbo sized "dozen."

By the way, I worked with an older guy who routinely said "six times ten to the 23; Ava Gardner's number" with a straight face.

 

[GuyBarry]

Right, like "a dozen" means twelve of anything. Twelve apples, twelve dwarves, twelve eggs. Avogadro's number is a super-jumbo sized "dozen."

You've got it exactly. The Avogadro constant is expressed in the units mol^-1. You might as well define "dozen" as an SI unit (symbol "doz") and specify the "dozenal constant" as 1.2 x 10¹ doz^-1.

Not really a "unit" in the sense that it's otherwise understood - just a gigantic multiplier.

 

[lpetrich]

I went over to https://www.bipm.org/en/measurement-units/rev-si/ and I found https://www.bipm.org/utils/en/pdf/si-revised-brochure/Draft-SI-Brochure-2018.pdf (5 February 2018).

The previous definition of the mole fixed the value of the molar mass of carbon 12, M(¹²C), to be exactly 0.012 kg/mol. According to the present definition M(¹²C) is no longer known exactly and must be determined experimentally. The value chosen for N_A is such that at the time of adopting the present definition of the mole, M(¹²C) was equal to 0.012 kg/mol with a relative standard uncertainty of 4.5 × 10⁻¹⁰.

So the atomic mass unit will be redefined as (1 gram) / (Avogadro's number), independent of carbon-12.

 

[GuyBarry]

I went over to https://www.bipm.org/en/measurement-units/rev-si/ and I found https://www.bipm.org/utils/en/pdf/si-revised-brochure/Draft-SI-Brochure-2018.pdf (5 February 2018).

So the atomic mass unit will be redefined as (1 gram) / (Avogadro's number), independent of carbon-12.

I really don't think that's correct. If you look at the top of page 29 it says "The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 of the mass of a free carbon 12 atom, at rest and in its ground state". So the amu is not being redefined.

Under the new definitions, the relative atomic mass of carbon-12 will remain exactly 12. However, the molar mass of carbon-12 will no longer be exactly 0.012 kg/mol. A consequence of this is that the molar mass constant, which was previously defined at exactly 0.001 kg/mol, will now be determined experimentally. It can still be taken as 1 g/mol for practical purposes. From Wikipedia:

Because the new SI definitions include a new definition of the mole through giving the Avogadro constant an exact numerical value, the value of the molar mass constant will no longer have an exactly defined value, assuming that the definition of a dalton (one twelfth of the rest mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state) does not change. Therefore, while still retaining with great accuracy a value of 1 g/mol, the molar mass constant will no longer be exactly defined at that value.

https://en.wikipedia.org/wiki/Molar_mass_constant