The nucleus is the very dense region consisting of protons and neutrons at the center of an
atom. It was discovered in 1911 as a result of Ernest Rutherford's interpretation of the
1909 Geiger–Marsden gold foil experiment performed by Hans Geiger and Ernest Marsden
under Rutherford's direction. The proton–neutron model of nucleus was proposed by Dmitry Ivanenko
in 1932. Almost all of the mass of an atom is located in the nucleus, with a very small
contribution from the electron cloud. The diameter of the nucleus is in the range
of 1.75 fm for hydrogen to about 15 fm for the heaviest atoms, such as uranium. These
dimensions are much smaller than the diameter of the atom itself, by a factor of about 23,000
to about 145,000. The branch of physics concerned with studying
and understanding the atomic nucleus, including its composition and the forces which bind
it together, is called nuclear physics.
Introduction History
The nucleus was discovered in 1911, as a result of Ernest Rutherford's efforts to test Thomson's
"plum pudding model" of the atom. The electron had already been discovered earlier by J.J.
Thomson himself, and knowing that atoms are neutral, Thomson postulated that there must
be a positive charge as well. In his plum pudding model, Thomson stated that an atom
consisted of negative electrons randomly scattered within a sphere of positive charge. Ernest
Rutherford later devised an experiment that involved the deflection of alpha particles
at a thin sheet of metal foil. He reasoned that if Thomson's model were correct, the
immense alpha particles would easily pass through the foil with very little deviation
in their paths. To his surprise, many of the particles were deflected at very large angles.
Because the mass of alpha particles is about 8000 times that of an electron, it became
apparent that a very strong force was present that allowed the particles to be deflected.
He realized that the plum pudding model could not be accurate and that the deflections of
the alpha particles could only be caused by a center of concentrated charge that contained
most of the atom's mass. Thus, the idea of a nuclear atom—an atom with a dense center
of positive charge—became justified. Etymology
The term nucleus is from the Latin word nucleus, a diminutive of nux, meaning the kernel inside
a watery type of fruit. In 1844, Michael Faraday used the term to refer to the "central point
of an atom". The modern atomic meaning was proposed by Ernest Rutherford in 1912. The
adoption of the term "nucleus" to atomic theory, however, was not immediate. In 1916, for example,
Gilbert N. Lewis stated, in his famous article The Atom and the Molecule, that "the atom
is composed of the kernel and an outer atom or shell"
Nuclear makeup
The nucleus of an atom consists of protons and neutrons bound by the nuclear force. These
baryons are further composed of subatomic fundamental particles known as quarks bound
by the strong interaction. Which chemical element an atom represents is determined by
the number of protons in the nucleus. Each proton carries a single positive charge, and
the total electrical charge of the nucleus is spread fairly uniformly throughout its
body, with a fall-off at the edge. Major exceptions to this rule are the light
elements hydrogen and helium, where the charge is concentrated most highly at the single
central point. This configuration is the same as for 1s electrons in atomic orbitals, and
is the expected density distribution for fermions in 1s states without orbital angular momentum.
As each proton carries a unit of charge, the charge distribution is indicative of the proton
distribution. The neutron distribution probably is similar.
While protons define the entire charge of a nucleus and, hence, its chemical identity,
neutrons are electrically neutral, but contribute to the mass of a nucleus to the same extent.
Neutrons explain the phenomenon of isotopes – varieties of a chemical element which
differ in atomic mass. Protons and neutrons
Protons and neutrons are fermions, with different values of the strong isospin quantum number,
so two protons and two neutrons can share the same space wave function since they are
not identical quantum entities. They sometimes are viewed as two different quantum states
of the same particle, the nucleon. Two fermions, such as two protons, or two neutrons, or a
proton + neutron can exhibit bosonic behavior when they become loosely bound in pairs.
In the rare case of a hypernucleus, a third baryon called a hyperon, with a different
value of the strangeness quantum number can also share the wave function. However, the
latter type of nuclei are extremely unstable and are not found on Earth except in high
energy physics experiments. The neutron has a positively charged core
of radius ≈ 0.3 fm surrounded by a compensating negative charge of radius between 0.3 fm and
2 fm. The proton has an approximately exponentially decaying positive charge distribution with
a mean square radius of about 0.8 fm. Forces
Nuclei are bound together by the residual strong force. The residual strong force is
a minor residuum of the strong interaction which binds quarks together to form protons
and neutrons. This force is much weaker between neutrons and protons because it is mostly
neutralized within them, in the same way that electromagnetic forces between neutral atoms
are much weaker than the electromagnetic forces that hold the parts of the atoms internally
together. The nuclear force is highly attractive at
the distance of typical nucleon separation, and this overwhelms the repulsion between
protons which is due to the electromagnetic force, thus allowing nuclei to exist. However,
because the residual strong force has a limited range because it decays quickly with distance,
only nuclei smaller than a certain size can be completely stable. The largest known completely
stable nucleus is lead-208 which contains a total of 208 nucleons. Nuclei larger than
this maximal size of 208 particles are unstable and become increasingly short-lived with larger
size, as the number of neutrons and protons which compose them increases beyond this number.
However, bismuth-209 is also stable to beta decay and has the longest half-life to alpha
decay of any known isotope, estimated at a billion times longer than the age of the universe.
The residual strong force is effective over a very short range and causes an attraction
between any pair of nucleons. For example, between protons and neutrons to form [NP]
deuteron, and also between protons and protons, and neutrons and neutrons.
Halo nuclei and strong force range limits The effective absolute limit of the range
of the strong force is represented by halo nuclei such as lithium-11 or boron-14, in
which dineutrons, or other collections of neutrons, orbit at distances of about ten
fermis. These nuclei are not maximally dense. Halo nuclei form at the extreme edges of the
chart of the nuclides—the neutron drip line and proton drip line—and are all unstable
with short half-lives, measured in milliseconds; for example, lithium-11 has a half-life of
less than 8.6 milliseconds. Halos in effect represent an excited state
with nucleons in an outer quantum shell which has unfilled energy levels "below" it. The
halo may be made of either neutrons [NN, NNN] or protons [PP, PPP]. Nuclei which have a
single neutron halo include 11Be and 19C. A two-neutron halo is exhibited by 6He, 11Li,
17B, 19B and 22C. Two-neutron halo nuclei break into three fragments, never two, and
are called Borromean nuclei because of this behavior. 8He and 14Be both exhibit a four-neutron
halo. Nuclei which have a proton halo include 8B and 26P. A two-proton halo is exhibited
by 17Ne and 27S. Proton halos are expected to be more rare and unstable than the neutron
examples, because of the repulsive electromagnetic forces of the excess proton(s).
Nuclear models Although the standard model of physics is
widely believed to completely describe the composition and behavior of the nucleus, generating
predictions from theory is much more difficult than for most other areas of particle physics.
This is essentially because perturbation theory, a widely used mathematical tool, is not applicable
to quantum chromodynamics at the energy scales relevant to the nucleus. As a result, experiments
have historically been compared to relatively crude models which are necessarily imperfect.
None of these models completely explain experimental data on nuclear structure.
The nuclear radius is considered to be one of the basic quantities that any model must
predict. For stable nuclei the nuclear radius is roughly proportional to the cube root of
the mass number of the nucleus, and particularly in nuclei containing many nucleons, as they
arrange in more spherical configurations: The stable nucleus has approximately a constant
density and therefore the nuclear radius R can be approximated by the following formula,
where A = Atomic mass number and r0 = 1.25 fm = 1.25 × 10−15 m. In this equation, the constant r0 varies by
0.2 fm, depending on the nucleus in question, but this is less than 20% change from a constant.
In other words, packing protons and neutrons in the nucleus gives approximately the same
total size result as packing hard spheres of a constant size into a tight spherical
or almost spherical bag. Liquid drop models
Early models of the nucleus viewed the nucleus as a rotating liquid drop. In this model,
the trade-off of long-range electromagnetic forces and relatively short-range nuclear
forces, together cause behavior which resembled surface tension forces in liquid drops of
different sizes. This formula is successful at explaining many important phenomena of
nuclei, such as their changing amounts of binding energy as their size and composition
changes, but it does not explain the special stability which occurs when nuclei have special
"magic numbers" of protons or neutrons. Shell models and other quantum models
A number of models for the nucleus have also been proposed in which nucleons occupy orbitals,
much like the atomic orbitals in atomic physics theory. These wave models imagine nucleons
to be either sizeless point particles in potential wells, or else probability waves as in the
"optical model", frictionlessly orbiting at high speed in potential wells.
In the above models, the nucleons may occupy orbitals in pairs, due to being fermions,
which allows to explain even/odd Z and N effects well-known from experiments. The exact nature
and capacity of nuclear shells differs from those of electrons in atomic orbitals, primarily
because the potential well in which the nucleons move is quite different from the central electromagnetic
potential well which binds electrons in atoms. Some resemblance to atomic orbital models
may be seen in a small atomic nucleus like that of helium-4, in which the two protons
and two neutrons separately occupy 1s orbitals analogous to the 1s orbital for the two electrons
in the helium atom, and achieve unusual stability for the same reason. Nuclei with 5 nucleons
are all extremely unstable and short-lived, yet, helium-3, with 3 nucleons, is very stable
even with lack of a closed 1s orbital shell. Another nucleus with 3 nucleons, the triton
hydrogen-3 is unstable and will decay into helium-3 when isolated. Weak nuclear stability
with 2 nucleons {NP} in the 1s orbital is found in the deuteron hydrogen-2, with only
one nucleon in each of the proton and neutron potential wells. While each nucleon is a fermion,
the {NP} deuteron is a boson and thus does not follow Pauli Exclusion for close packing
within shells. Lithium-6 with 6 nucleons is highly stable without a closed second 1p shell
orbital. For light nuclei with total nucleon numbers 1 to 6 only those with 5 do not show
some evidence of stability. Observations of beta-stability of light nuclei outside closed
shells indicate that nuclear stability is much more complex than simple closure of shell
orbitals with magic numbers of protons and neutrons.
For larger nuclei, the shells occupied by nucleons begin to differ significantly from
electron shells, but nevertheless, present nuclear theory does predict the magic numbers
of filled nuclear shells for both protons and neutrons. The closure of the stable shells
predicts unusually stable configurations, analogous to the noble group of nearly-inert
gases in chemistry. An example is the stability of the closed shell of 50 protons, which allows
tin to have 10 stable isotopes, more than any other element. Similarly, the distance
from shell-closure explains the unusual instability of isotopes which have far from stable numbers
of these particles, such as the radioactive elements 43 and 61, each of which is preceded
and followed by 17 or more stable elements. There are however problems with the shell
model when an attempt is made to account for nuclear properties well away from closed shells.
This has led to complex post hoc distortions of the shape of the potential well to fit
experimental data, but the question remains whether these mathematical manipulations actually
correspond to the spatial deformations in real nuclei. Problems with the shell model
have led some to propose realistic two-body and three-body nuclear force effects involving
nucleon clusters and then build the nucleus on this basis. Two such cluster models are
the Close-Packed Spheron Model of Linus Pauling and the 2D Ising Model of MacGregor.
Consistency between models
As with the case of superfluid liquid helium, atomic nuclei are an example of a state in
which both "ordinary" particle physical rules for volume and non-intuitive quantum mechanical
rules for a wave-like nature apply. In superfluid helium, the helium atoms have volume, and
essentially "touch" each other, yet at the same time exhibit strange bulk properties,
consistent with a Bose–Einstein condensation. The latter reveals that they also have a wave-like
nature and do not exhibit standard fluid properties, such as friction. For nuclei made of hadrons
which are fermions, the same type of condensation does not occur, yet nevertheless, many nuclear
properties can only be explained similarly by a combination of properties of particles
with volume, in addition to the frictionless motion characteristic of the wave-like behavior
of objects trapped in Erwin Schrödinger's quantum orbitals.
See also
References
External links The Nucleus – a chapter from an online textbook
The LIVEChart of Nuclides – IAEA in Java or HTML
Article on the "nuclear shell model," giving nuclear shell filling for the various elements.
Accessed Sept. 16, 2009. Timeline: Subatomic Concepts, Nuclear Science
& Technology.