Does an atom mostly consist of empty space?
The view that an atom mostly consist of empty space stems from the old
times when Bohr's atomic model (as a miniature planetary system in
which electrons surround the nucleus) was the best picture of what an
atom is like.
But there are no electron particles moving around an atom.
One cannot view the electrons as little balls moving inside a molecule
and somehow avoiding falling into a nucleus. Such a configuration
would be unstable. The nuclei would attract little charged balls until
they fall into them.
But it is very well understood why atoms are stable - the ground state
is a delocalized stationary state of the electrons in an atom, a state
living indefinitely (unless the nucleus decays). In terms of quantum
field theory, the space is filled by the electron field. The resulting
electron density can be calculated by quantum mechanics. Indeed, this
is one of the outputs chemists are interested in when they use quantum
chemistry packages like GAMESS.
Electrons behaving as particles (in the sense of being localized at approximately one place) only exist in situations where one may consider the field theory in the limit of geometric optics (cf. photons as particles of light), so that one can speak meaningfully of their paths. See, e.g.,
which presents a phenomenological view,
which derives geometrical electron optics from the Dirac equation, or the book
which contains engineering details for electron beams. Geometric optics is an essentially macroscopic view not applicable inside atoms or small molecules. To measure the position of a single electron, you need to make it reach a localized detector such as a Geiger counter, thereby localizing it. But it is impossible to make a measurement of an electron bound in a molecule. What one can measure there is only the charge distribution. Thus electrons show up as particles only under particular circumstances; e.g., in detectors such as Geiger counters.
There is no empty space around a nucleus, as in Bohr's superseded model.
The electrons make up a tiny proportion of the mass of an atom, while
the nucleus makes up the rest. The nucleus makes up a tiny proportion
of the space occupied by an atom, while the electrons make up the rest.
According to quantum electrodynamics, the space is filled by an
electron field around the nucleus which neutralizes its charge
and fills the space defining the atom size. What is displayed by a
field ion microscope is the
boundary of this field. But this boundary is not perfectly defined
but a bit fuzzy, more like the surface of a piece of fur or of a cloud.
The electrons are therefore rather like a very low-density glue-like
viscous fluid surrounding the nuclei and making up the spatial extent
of the atom, transparent for neutrons but not for other electrons.
Chemists draw the shape of these fluid clouds (more precisely, the
electron density) as orbitals. See, e.g.,
The picture of an atom being mostly empty stems from the childhood of
atomic structure analysis, where most of the atom's extension was found
to be transparent for alpha rays, and the
early models
explained that by pointlike nuclei and electrons.
Similarly the picture of a proton or neutron being essentially empty
apart from three quarks embedded in it arises because deep inelastic
scattering shows that protons are essentially transparent for very
energetic electrons, except when the latter meet an almost pointlike
quark.
But both pictures are quite limited:
We don't think glass doesn't occupy space because it is transparent
for light, or that only the bones of our bodies occupy space because
the remainder is transparent for X-rays. So why should we think of the
electronic fluid surrounding nuclei not to occupy space simply because
it is transparent to alpha rays, or of the meson and gluon fluid in
which the quarks are embedded not to occupy space simply because it is
transparent to fast leptons?
Glass is hard because it is occupied by a matter field that resists
other matter (though not photons).
Atoms are even harder because it is occupied by a matter field that
resists other matter (though not alpha rays).
Protons and neutrons are even harder because they are occupied by a
matter field that resists other matter (though not fast leptons).
What we touch is an effective field whose extension is created by the
electrons, and whose mass is created by the nuclei (or, on an even
deeper level, by constituent quarks).
Indeed, most of the mass in ordinary matter is due to the strong
interaction, generated dynamically through dynamical symmetry breaking.
This results in constituent quark masses. These approximately add up
to proton and neutron masses, and from these to the masses of atoms
and molecules, and finally of the solids and fluids that make up our
everyday world. The deviations are due to the fact that mass and
energy are inter-convertible to some extent, and that the binding
energy takes away a bit from particles bound together.
In macroscopic neutral matter, the effective fields are one mass field
for each participating chemical substance, a stress field, a momentum
field, an energy field. and their conjugate thermodynamic fields.
If two atoms or molecules touch, the volumes occupied by their electron
fields touch, and repel each other, while at a slightly (but not much)
larger distance there is a slight attraction, the van der Waals
attraction, responsible for the formation of liquids. Thus touching is
a real effect. The nuclei don't touch each other but the atoms and
molecules do.
More precisely, the residual force between electrons bound in two
different atoms whose nuclei are at distance r consists of two terms:
(i) the attractive van der Waals force, which decays with distance
like 1/r^7, hence is immeasurable at the distance of 1m but noticeable
as friction at close to contact distance. (It is attractive although
the electrons carry the same negative charge since it also contains
the effects of the positive charge of the nucleus.)
(ii) the repulsive (approximate hard core) force, which decays with
distance like 1/r^11 (or so), hence is immeasurable already at
distances just beyond contact but gets very strong at contact distance,
and ensures that solid matter cannot penetrate other solid matter.
The same holds for fluid matter - liquids and gas, but there the
molecules are so weakly held together that the matter simply gives way
to the contact motion.
See also How do atoms and molecules look like?
Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ