Download Quantum Theory

Quantum Theory
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The Quantum Model of the Atom
Heisenberg Uncertainty Principle:
This idea involves the detection of electrons.
Electrons are detected by their interaction with photons
(a particle of electromagnetic radiation)
• Because photons have about the same energy as
electrons, any attempt to locate a specific electron off its
course.
• The Heisenberg Uncertainty Principle states that it is
impossible to determine simultaneously both the
position and velocity of an electron or any other
particle.
• The Schrödinger Wave Equation:
• In 1926, Erwin Schrödinger used the hypothesis that electrons have
a dual wave particle nature to develop an equation that treated
electrons with atoms as waves.
• Together with the Heisenberg Uncertainty Principle, the Schrödinger
Wave Equation helped develop the Modern Quantum Theory.
• The quantum theory describes mathematically the wave properties
of electrons and other very small particles.
• Solutions to the Schrödinger wave equation are known as wave
functions.
• Wave functions, though, give on the probability of finding an electron
at a given place around the nucleus.
• Electrons can exist in certain regions called orbitals; orbitals are
three dimensional region around the nucleus that indicate the
probable location of an electron.
• Atomic Orbitals and Quantum Numbers:
• According to the Schrödinger Equation, electrons in
atomic orbitals also have quantized energies. In order to
describe orbitals, scientist use quantum numbers.
• Quantum numbers specify the properties of atomic
orbitals and the properties of electrons in orbitals.
• The 1st three quantum numbers indicate: main energy
level, shape, and orientation of an orbital.
• The 4th , the spin quantum number, describes a
fundamental state of the electron that occupies the
orbital.
• Principle Quantum Number:
• The principle quantum number, symbolized by “n”,
indicates the main energy level occupied by the electron.
• Values of “n” are positive integers only: 1,2,3 . . .
• An electron for which n=1 occupies the first, or lowest,
main energy level and is located closest to the nucleus.
• More than one electron can have the same “n” value.
These electrons are said to be in the same electron
shell. The total number of orbitals that exist in a given
shell or main energy level is equal to n2.
• Angular Momentum Quantum Number:
• The angular momentum quantum number, symbolize by “l”,
indicates the shape of the orbital.
• For a specific main energy level, the number of orbital shapes
possible is equal to “n”. The values of “l” allowed are zero and all
positive integers, less than or equal t n-1.
• Depending on the value of ‘l” an orbital is assigned a letter as shown
in the table below.
• “l”
Letter
• 0
s
• 1
p
• 2
d
• 3
f
• S orbitals are spherical, P orbitals are dumb-bell shapes, D orbitals
are more complex, F orbitals are too complex to discuss here.
• In the 1st energy level, n=1, there is only one sublevel possible --an s orbital,
• The 2nd energy level, n=2, has two sublevels --- s & p orbitals.
• The 3rd energy level, n=3, has three sublevels --- s, p & d orbitals.
• The 4th energy level, n=4, has four sublevels --- s, p, d, & f orbitals.
• In an nth main energy level, there are n sublevels.
• Each atomic orbitals is designated by the principal quantum number
followed by the letter of the sublevel. For example, the 1st sublevel
is the s orbitals in the first main energy level, while the 2p sublevel is
the set of p orbitals in the second main energy level.
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Magnetic Quantum Number:
Atomic Orbitals can have the same shape but different orientation around the nucleus.
The magnetic quantum number, symbolized by “m”, indicates the orientation of the orbital around
the nucleus.
Because the s orbital is spherical and is centered around the nucleus, it has only one possible
orientation. This corresponds to a magnetic quantum number of m=0. There is, therefore, only one
s orbital in each sublevel.
(refer to FIGURE 5-15 in your textbook – p. 133)
The lobes of the p orbital can extend along the x, y, or z axis of a 3-D coordinate system.
There are 3 p orbitals in each p sublevel, which are labeled as Px, Py, Pz orbitals. These
correspond to the values of m=-1, m=0, m=+1.
(refer to FIGURE 5-16 in your textbook – p.133)
There are five different d orbitals in each d sublevel. The five orientations correspond to :
m=-2, m=-1, m=0, m=+1, m=+2
(refer to the drawings in the class notes—transparencies)
There are seven different f orbitals in each f sublevel. The # of orbitals at each main energy level
equals the square of the principle quantum number (n2).
• Spin Quantum Number:
• An electron spins in one or two possible
directions. As it spins, it creates a
magnetic field. The spin quantum number
has only two possible values --- (+1/2 , 1/2)--- which indicate the two spin states of
an electron in an orbital. A single orbital
can hold max. of 2 electrons, which must
have opposite spins.
• Electron Configurations:
• The arrangement of electrons in an atom is
known as the atom’s electron configuration.
• Because atoms of different elements have
different numbers of electrons, a distinct electron
configuration exists for the atoms of each
element. The lowest energy arrangement of the
electrons is called the element’s ground state
electron configuration.
• Electron Configuration Rules:
• RULE #1 – Aufbau Principle: --- An electron occupies the lowest
energy orbital that can receive it. The orbital with the lowest energy
is the 1s orbital (1s, 2s, 2p, 3s, etc.)
• Rule #2 – Pauli Exclusion Principle:--- No two electrons in the
same set of four quantum numbers. Thismans an orbital can hold
two electrons of opposite spin.
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• Rule #3Hund’s Rule:--- Orbitals of equal energy are each occupied
by one electron before any orbital is occupied by a second electron,
and all electrons in singly occupied orbitals must have the same
spin.
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• Four (4) Types of Notation:
• 1) Orbital Notation:
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H ____
He ___
Li ____ ____
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1s
1s
1s
2s
• 2) Electron-Configuration Notation:
• H= 1s1
He= 1s2
Li= 1s2 2s1
Be= 1s2 2s2
• 3) Noble Gas Notation:
• Na = [Ne] 3s1
Mg= [Ne] 3s2
Al=
[Ne] 3s2 3p1
• 4) Electron Dot Notation:
• Electron dot notation is an electron configuration
notation in which only the valence electrons
(electrons in the outer-most energy level--- that
are available to be lost, gained, or shared to
form compounds) of an atom of a particular
element are shown, indicated by dots placed
around the element’s symbol.
• For example: Sulfur
• S= 1s2 2s2 2p6 3s2 3p4 may be written as: