Re: how is it that the Atomic Mass Unit is less than either the
- From: "Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx>
- Date: Wed, 20 Sep 2006 09:29:50 +0000 (UTC)
On Tue, 19 Sep 2006, robert bristow-johnson wrote:
the amu is defined to be 1/12 the mass of a carbon-12 atom, i presume
complete with 6 protons, 6 neutrons, and 6 electrons.
even if the electrons weighed nothing, each proton and neutron is more
than the amu so it must add to more than 12 amu. how can this be?? i
know that this is a definition, but it seems to me that the definition
does not square with CODATA values of the most massive components of a
carbon-12 atom and the conservation of mass principle. how does
sticking these 6 neutrons and 6 protons together, toss in 6 electrons
and maybe some binding energy/c^2 add up to less than the total? i
don't get it.
i had always assumed that the amu was somewhere nearly halfway between
the proton and neutron rest mass, but it's less than either. how can
that be?
can someone make sense of this?
Very simple; the mass of a system is not the sum of the masses of the
components. Energy matters, E=mc^2 and all that. You need to _add_ energy
to carbon to break it into isolated protons, neutrons, and electrons. That
means that the energy of a single carbon atom is less than that of its
individual constituents. Thus, there is a _negative_ amount of energy -
the binding energy - associated with assembling them into carbon. E=mc^2
with a negative energy means that that amount of negative energy has a
negative mass, and the mass of a carbon atom is less than the sum of the
masses of 6 electrons + 6 protons + 6 neutrons.
Strange? Maybe so. But consider the best(?) definition of rest mass we
have: the magnitude of the energy-momentum 4-vector, with appropriate unit
conversion as required. For example, take 1 photon, and you get zero rest
mass. Take two identical photons going in opposite directions, and since
the total momentum is zero, but the energy is not, the rest mass cannot be
zero.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.
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