Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Mass



I asked:
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?

to which John D. answered:
The proposal is to count the atoms. I don't see what
concentration has to do with it.

OK, but you also write that:
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.

So we measure the number in the unit cell, and then assume the
concentration is the same throughout the sample, right?

> 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.

OK. You need to measure the number (in a unit cell) and the volume of
the sample and the unit cell. From these measurements, you get the
mass. Apparently, we are saying the same thing.

[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.

Yeh, I agree, but you could place the balance in a evacuated chamber to
get rid of buoyancy effects. You can't do much to get rid of the
gravitational effects. Displacing the center of mass by delta r causes
a change in gravitational force equal to:
d(GMm/r^2)/dr (delta r) = GMm (-2/r^3) (delta r)
= GMm/r^2 (-2/r) (delta r)
or a fractional change of 2*(delta r)/r. For 1 cm difference in center
of mass, this causes a relative difference in measured mass of
2e-2/6.37e6 ~ 3e-9. So, for a 1-kg standard, the difference is 3
micrograms. I know this seems tiny and for almost all practical
purposes irrelevant but I thought it was pertinent to the discussion
about measuring inertial vs. gravitational mass. I also think balances
are available that can measure with a precision exceeding 1e-9. If you
happen to be using one, it helps to know if you're measuring inertial
mass or not.

____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301