1. ELECTRON CLOUD MODEL
Electron Density and Orbital Shapes
Atomic orbitals are mathematical
descriptions of where the electrons in an
atom (or molecule) are most likely to be
found. These descriptions are obtained by
solving an equation known as the
Schrödinger equation, which expresses
our knowledge of the atomic world. As the
angular momentum and energy of an
electron increases, it tends to reside in
differently shaped orbitals. The orbitals
corresponding to the three lowest energy
states are s, p, and d, respectively. The
illustration shows the spatial distribution of electrons within these orbitals. The
fundamental nature of electrons prevents more than two from ever being in the
same orbital. The overall distribution of electrons in an atom is the sum of many such
pictures. This description has been confirmed by many experiments in chemistry and
physics, including an actual picture of a p-orbital made by a Scanning Tunneling
Microscope.
Electron Cloud
Most of the physical and chemical properties of atoms, and hence of all matter, are
determined by the nature of the electron cloud enclosing the nucleus.
The nucleus of an atom, with its positive electric charge, attracts negatively charged
electrons. This attraction is largely responsible for holding the atom together. The
revolution of electrons about a nucleus is determined by the force with which they
are attracted to the nucleus. The electrons move very rapidly, and determination of
exactly where any particular one is at a given time is theoretically impossible (see
Uncertainty Principle). If the atom were visible, the electrons might appear as a
cloud, or fog, that is dense in some spots, thin in others. The shape of this cloud and
the probability of finding an electron at any point in the cloud can be calculated from
the equations of wave mechanics (see Quantum Theory). The solutions of these
equations are called orbitals. Each orbital is associated with a definite energy, and

2. each may be occupied by no more than two electrons. If an orbital contains two
electrons, the electrons must have opposite spins, a property related to the angular
momentum of the electrons. The electrons occupy the orbitals of lowest energy first,
then the orbitals next in energy, and so on, building out until the atom is complete
(see Atom).
The orbitals tend to form groups known as shells (so-called because they are
analogous to the layers, or shells, around an onion). Each shell is associated with a
different level of energy. Starting from the nucleus and counting outward, the shells,
or principal energy levels, are numbered 1, 2, 3, … , n. The outer shells have more
space than the inner ones and can accommodate more orbitals and therefore more
electrons. The nth shell consists of 2n-1 orbitals, and each orbital can hold a
maximum of 2 electrons. For example, the third shell contains five orbitals and holds
a maximum of 10 electrons; the fourth shell contains seven orbitals and holds a
maximum of 14 electrons. Among the known elements, only the first seven shells of
an atom contain electrons, and only the first four shells are ever filled.
Each shell (designated as n) contains different types of orbitals, numbered from 0 to
n-1. The first four types of orbitals are known by their letter designations as s, p, d,
and f. There is one s-orbital in each shell, and this orbital contains the most firmly
bound electrons of the shell. The s-orbital is followed by the p-orbitals (which always
occur in groups of three), the d-orbitals (which always occur in groups of five), and
finally the f-orbitals (which always occur in groups of seven). The s-orbitals are
always spherically shaped around the nucleus; each p-orbital has two lobes
resembling two balls touching; each d-orbital has four lobes; and each f-orbital has
eight lobes. The p-, d-, and f-orbitals have a directional orientation in space, but the
spherical s-orbitals do not. The three p-orbitals are oriented perpendicular to one
another along the axis of an imaginary three-dimensional Cartesian (x, y, z)
coordinate system. The three p-orbitals are designated px, py, and pz, respectively.
The d- and f-orbitals are similarly arranged about the nucleus at fixed angles to one
another.
When elements are listed in order of increasing atomic number, an atom of one
element contains one more electron than an atom of the preceding element (see
Chemical Elements). The added electrons fill orbitals in order of the increasing
energy of the orbitals. The first shell contains the 1s orbital; the second shell contains
the 2s orbital and the 2p orbitals; the third shell contains the 3s orbital, the 3p
orbitals, and the 3d orbitals; the fourth shell contains the 4s orbital, the 4p orbitals,
the 4d orbitals, and the 4f orbitals.
After the two innermost shells, certain orbitals of outer shells have lower energies
than the last orbitals of preceding shells. For this reason, some orbitals of the outer
shells fill before the previous shells are complete. For example, the s-orbital of the

3. fourth shell (4s) fills before the d-orbitals of the third shell (3d). Orbitals generally fill
in this order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s.
In a notation frequently used to describe the electron configuration of an element, a
superscript after the orbital letter gives the number of electrons in that orbital. Thus,
1s22s22p5 means that the atom has two electrons in the 1s orbital, two electrons in
the 2s orbital, and five electrons in the 2p orbitals.
Neutral atoms with exactly eight electrons in the outer shell (meaning the s- and p-
orbitals of the outer shell are filled) are exceptionally stable. These neutral atoms are
atoms of the noble gases, which are so stable that getting them to chemically react
with other elements is very difficult. The unusual stability of the noble-gas electron
structures is of great importance in chemical bonding and reactivity. All other
elements tend to combine with each other in such a way as to imitate this stable
structure. The structure of helium is 1s2; neon adds another stable shell, 2s22p6, to
this; argon adds the orbitals 3s23p6; krypton adds the orbitals 4s23d104p6; and xenon
adds the orbitals 5s24d105p6 (the s-orbital fills before the d-orbital of the previous
shell).
A.Electron Orbitals
Electron Density and Orbital Shapes
Atomic orbitals are mathematical descriptions of where the electrons in an
atom (or molecule) are most likely to be found. These descriptions are obtained
by solving an equation known as the Schrödinger equation, which expresses our
knowledge of the atomic world. As the angular momentum and energy of an
electron increases, it tends to reside in differently shaped orbitals. The orbitals
corresponding to the three lowest energy states are s, p, and d, respectively.
The illustration shows the spatial distribution of electrons within these orbitals.
The fundamental nature of electrons prevents more than two from ever being
in the same orbital. The overall distribution of electrons in an atom is the sum
of many such pictures. This description has been confirmed by many
experiments in chemistry and physics, including an actual picture of a p-orbital
made by a Scanning Tunneling Microscope.
Atomic Orbital Shapes
Atomic orbitals are mathematical descriptions of where the electrons in an
atom (or molecule) are most likely to be found. These descriptions are obtained
by solving an equation known as the Schrödinger equation, which expresses our

4. knowledge of the atomic world. As the angular momentum and energy of an
electron increases, it tends to reside in differently shaped orbitals. This
description has been confirmed by many experiments in chemistry and physics,
including an actual picture of a p-orbital made by a scanning tunneling
microscope.
Quantum Description of Electrons
Scientists describe the properties of an electron in an atom with a set of numbers
called quantum numbers. Electrons are a type of particle known as a fermion,
and according to a rule of physics, no two fermions can be exactly alike. Each
electron in an atom therefore has different properties and a different set of
quantum numbers. Electrons that share the same principal quantum number
form a shell in an atom. This chart shows the first three shells. The two electrons
that share the principal quantum number 1 form the first shell. One of these
electrons has the quantum numbers 1, s, 0, 1/2, and the other electron has the
quantum numbers 1, s, 0, -1/2.
Scientists cannot simultaneously measure both the exact location of an electron and
its precise speed and direction, so they cannot measure the path a specific electron
takes as it orbits the nucleus. The law of physics governing this phenomenon is called
the uncertainty principle. Scientists can, however, determine the area an electron
will probably occupy, and the probability of finding the electron at some place inside
this area. A map of this area and its probabilities forms a cloudlike pattern known as
an orbital. Each orbital can contain two electrons, but these electrons can not have
identical properties, so they must spin in opposite directions. Orbitals are grouped
into shells, like the layers of an onion, around the nucleus. Each shell can contain a
limited number of orbitals, which means that each shell can contain a limited
number of electrons. Each shell corresponds to a certain level of energy, and all the
electrons in the shell have this same level of energy. As the shells get farther from
the nucleus, they can contain more electrons, and the electrons in the shells have
higher energy. See also Chemistry: Electron Cloud.
Light Absorption and Emission
When a photon, or packet of light energy, is absorbed by an atom, the atom
gains the energy of the photon, and one of the atom’s electrons may jump to a
higher energy level. The atom is then said to be excited. When an electron of
an excited atom falls to a lower energy level, the atom may emit the electron’s
excess energy in the form of a photon. The energy levels, or orbitals, of the

5. atoms shown here have been greatly simplified to illustrate these absorption
and emission processes. For a more accurate depiction of electron orbitals,
When an atom’s energy is at its minimum, it is said to be in a ground state. In this
ground state, the atom’s electrons occupy the innermost available shells, those
closest to the nucleus. When atoms are excited by heat, by an electric current, or by
light or some other form of radiation, the atoms’ electrons can acquire energy and
jump from an inner to an outer shell, leaving a vacancy in the inner shell. The atom
seeks to shed this surplus energy, leading the electron in the outer orbit to fall back
down to an inner vacancy. As it falls, the electron releases energy in the form of a
photon, a tiny flash of light. The color of the light depends on the amount of energy
emitted.
Spectral Lines of Atomic Hydrogen
When an electron makes a transition from one energy level to another, the
electron emits a photon with a particular energy. These photons are then
observed as emission lines using a spectroscope. The Lyman series involves
transitions to the lowest or ground state energy level. Transitions to the second
energy level are called the Balmer series. These transitions involve frequencies
in the visible part of the spectrum. In this frequency range each transition is
characterized by a different color.
When an electron moves to a different shell, it does not gradually go from one shell
to another, but instead jumps directly to the other shell. These jumps are like steps
on a staircase (and are different from a smooth incline, or hill). The electron also
absorbs or emits the energy to make jumps in steps. It cannot gradually build up or
lose energy, but must instantly absorb the exact amount of energy needed to make a
certain jump, or instantly emit the exact amount needed to fall to a lower shell. Each
element has a different pattern of allowed jumps within its electronic structure, so
the element’s atoms can only absorb or emit a distinct set of energies, or spectrum
of colors. In this way, a scientist can tell which elements are present in a sample by
looking at the colors absorbed or emitted when the sample is excited by heat,
electricity, or light. See also Spectroscopy.