Re: Mass

[John Denker <jsd@AV8N.COM>]

Robert Cohen wrote:
> I'm
> asking how I would know that the mass of sample is 1 kg.  It just
> appears to me that we don't count the number of atoms but rather the
> concentration of atoms.  Am I wrong about that?

The proposal is to count the atoms.  I don't see what
concentration has to do with it.

First, the motivation:  The goal is to get rid of _artifact_
standards and replace them with _physical_ standards, i.e.
_natural_ standards.

A while back, there used to be an artifact meter, namely
the length between two marks on a metal bar stored at Paris.
Then one fine day they disestablished the artifact meter,
and defined a new meter to be the distance that light
travels in a certain exact, defined amount of time.  Of
course they chose the time such that the new meter was
consistent with the old meter.  The new meter is much more
precisely known.  It is also a whole lot more portable:
accurate time signals can be easily propagated, and now
if you can measure time you can calibrate your local
secondary standard of length.  (As part and parcel of this
exercise, the speed of light is now an exact, defined
quantity.)

Now the artifact kilogram is the only remaining important
artifact in the SI system.  There are excellent philosophical
as well as practical motivations for disestablishing it
and replacing it with a natural, physical standard.  This
procedure for doing this will be analogous to what happened
to the meter.  Right now, Avogadro's number is a measurable
quantity based on the idea that a mole of 12C has a mass =
12 grams.  But we can turn that around.  We can choose an
xact, defined value for Avogadro's number, and then define
the kilogram to preserve the notion that a mole of 12C has
mass = 12 grams.  That's the primary key idea.

This scheme is predicated on being able to count atoms
accurately.  You need to count a *lot* of atoms in order
to construct a secondary mass-standard that is large
enough to be useful.  The proposal on the table is to
count atoms by dividing the volume of a crystal by the
volume of the unit cell.  The latter can be found by
means of xray crystallography ... we know that the
dispersion of a diffraction grating depends in a simple
way on the spacing of the grating.

This scheme is nowhere near ready for prime time, for
a number of reasons:
 -- dispersion depends also on the xray wavelength, which is
  not easily measured to the desired accuracy.
 -- it is more practical to grow large Si crystals rather than
  large diamonds, so you will need to know the Si/C mass ratio
  to high accuracy (or risk annoying chemists, who rely
  on 12C as their mass standard).
 -- there are isotopes of Si to worry about ... they change
  the mass without much change in lattice spacing.
 -- probably scads of other technical difficulties I don't
  know about.

> If not, it appears we must use the volume to determine the mass,
> assuming we know the mass of each atom (which we would know based
> upon the masses of the protons, neutrons and electrons and the
> mass-equivalence of the binding energy).

Actually we don't need to know the mass of the progons etc.
or the binding energy.  If the program succeeds, then the
mass of 12C becomes a _defined_ quantity.

> If so, why not just define 1 kg of
> silicon in terms of the volume of the sample?  Why not use the mass of
> each atom and the configuration of silicon to obtain the density and
> then define 1 kg in terms of the volume and density of silicon?

You could ... but you would need to think real hard about what
volume to establish as the standard, lest you choose something
that is inconsistent with the previous values of the kilogram
and/or Avogadro's number.  Also of course you would need to
specify the conditions (STP or whatever) at which the density
is obtained.

> [By the way, if a balance really measures inertial mass, it wouldn't
> matter where the object's center of mass is, right?  Keep in mind that
> the earth's gravitational field decreases with height.]

Is this a significant problem?  How tall are the objects you
are weighing?

I suspect other non-idealities e.g. buoyancy are more worth
worrying about.