10.7 The Hydrogen Orbitals
 In the Wave Mechanical model of the
atom an orbital represents the space
around the nucleus occupied by an
electron.
 An orbital is the probability distribution
for an electron where it can be found
90% of the time (see fig 10.20, 10.24,
10.25).
• Hydrogen orbitals
– The discrete energy levels of
hydrogen are called principal
energy levels and are labeled with
an integer (1, 2, 3, 4 …)
– The principal levels have sublevels
which contain spaces (orbitals) for
electrons (fig 10.22).
Ex: 1s, 2s, 2p, 3s, 3d, etc
•
•
•
•
1 = energy level, s = shape (sphere)
2 = energy level, s = shape (sphere)
2 = energy level, p = shape (lobed)
3 = energy level, d = shape (fig 10.28)
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– energy level 1 has one sublevel:
• 1s has one orbital
– energy level 2 has two sublevels:
• 2s has one orbital
• 2p has three orbitals (2px, 2py, 2pz)
– energy level 3 has three sublevels:
• 3s has one orbital
• 3p has three orbitals (3px, 3py, 3pz)
• 3d has five orbitals (fig 10.28)
– energy level 4 has four sublevels:
•
•
•
•
4s has one orbital
4p has three orbitals (4px, 4py, 4pz)
4d has five orbitals
4f has 7 orbitals
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– hydrogen also has energy levels
above level 4
– an orbital is potential space for an
electron
– energy can excite the electron in
the 1s orbital (ground state) and
move it to a higher energy level (2s,
2p, 3s, etc.) further from the
nucleus
– when the excited electron returns to
its lower energy orbital it gives off a
photon of light with equal energy to
the amount of energy it absorbed
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10.8 The Wave-Mechanical Model:
Further Development
• Wave mechanics: Matter as waves
– Light (photons) can be demonstrated to
behave as either waves or particles.
– Similarly, matter can behave as waves.
– In 1923 Louis de Broglie proposed that a
particle of mass can have wavelike
properties. This meant that electrons can
have a wave-particle duality, much like
light does.
– In 1926 Erwin Schroedinger worked out
the mathematics of depicting electrons as
waves:
• An electron could only exist in different regions
around a nucleus, meaning its energy was
quantized.
• The regions of stability were a complex
interplay of the electrostatic field generated by
charged electrons and atomic nuclei.
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• The wave mechanical model applies
to all atoms, not just hydrogen.
• Electrons (in ground states, i.e.,
unexcited) are arranged in an atom’s
orbitals following specific rules.
– The Pauli exclusion principle: no more
than two electrons of opposite spin
(designated by ↑ ↓ ) can occupy an
atomic orbital.
– The Aufbau principle: electrons fill
orbitals at the lowest possible energy
level before filling higher levels (e.g., 1s
before 2s, 2p before 3s, etc.)
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Order of filling orbitals
– Hund’s Rule: electrons of the same
spin are added to each orbital in a
sublevel before a second electron of
opposite spin is added
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•
Principal Components of the
Wave Mechanical Model
(see pg 293)
1. Atoms have a series of principal
energy levels, n; which can equal
1, 2, 3, 4, . . .
2. The energy of the level increases
as n increases.
3. Each principal energy level
contains one or more types of
orbitals, called sublevels.
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4. The number of sublevels in a given
principal energy level equals n.
level 1 contains 1 sublevel
level 2 contains 2 sublevels
level 3 contains 3 sublevels
and so on . . .
5. The n value is always followed
with a letter indicating the shape
of the orbital (s, p, d, f ).
6. An orbital can be empty or contain
one or two electrons with opposite
spin.
7. The shape of the orbital is a
probability distribution for an
electron in that orbital.
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10.9 Electron Arrangements in First
Eighteen Elements
• Electrons are placed in various orbitals
starting with n = 1, and continuing with n = 2,
n = 3, and so on.
• The orbital closest to the nucleus is the 1s.
As n increases, the orbital becomes larger
and the electron occupies space further from
the nucleus.
• Electron configurations show the electrons
occupying orbitals in each energy level.
• Orbital diagrams (box diagrams) show
orbitals as boxes grouped by sublevels with
arrows showing electrons.
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• Valence electrons are the electrons in the
outermost (highest) principal energy level of
the atom.
– Example:
– These electrons are involved in bonding
between atoms
• Core electrons are the electrons not involved
in bonding atoms to each other.
– Example
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10.10 Electron Configurations and
the Periodic Table
• The electron configuration of any element can be
determined by understanding its position in the
periodic table. See fig 10.31
• Some transition metals, however, do not follow the
general pattern for placing electrons in orbitals (for
reasons not discussed here).
• Summary of Wave-Mechanical Model and ValenceElectron Configurations.
– The W-M model pictures electrons in an atom
arranged in orbitals, with each orbital holding two
electrons.
– The same type of orbitals recur in going from one
principal energy level to another.
– This means valence electron configurations recur
periodically. See fig 10.34
– Elements in particular groups (such as the alkali
metals, halogens, etc.) have the same valence
electron arrangement and, therefore, share similar
chemical properties.
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