Transcript The Quantum Mechanical Model of the Atom

The Quantum Mechanical Model
of the Atom
What’s wrong with the Bohr model?
Heisenberg, de Broglie, Schrodinger
• Developed a model of the atom based on wave
mechanics (quantum mechanics)
– The electron bound to the nucleus seemed similar to a
standing wave
• De Broglie – originated the idea that the electron
also shows wave properties (in addition to
particulate properties)
• Schrodinger – put emphasis on the wave
properties of the electron
Standing Waves & Musical Instruments
• A string attached to a violin or guitar
vibrates to produce a musical tone
• The waves are “standing” because they are
stationary, they don’t travel the length of the
string
Figure 7.9
•The dots indicate the nodes, or points
of zero lateral (sideway) displacement,
for a given wave.
•There are limitations on the allowed
wavelengths of the standing wave.
•Each end of the string is fixed, so there
is always anode at each end
• There must be a whole number of half
wavelengths in any of the allowed
motions of the string
From Music Strings to Electrons
• The electron in the hydrogen atom is imagined to be a
standing wave.
• Only certain circular orbits have a circumference into
which a whole number of wavelengths of the standing
electron wave will “fit”
• All other orbits would produce destructive interference of
the standing electron wave and are not allowed.
• Explained by Schrodinger’s equation: H=E 
Schrodinger’s equation: H=E
•  is called the wave function (a function of the coordinate (x, y, and z)
of the electron’s position in three-dimensional space
• H is set of mathematical instructions called an operator that produce
the total energy of the atom when they are applied to the wave
function.
• E is the total energy of the atom (the sum of the potential energy due to
the attraction between the proton and electron and the kinetic energy of
the moving electron)
• When the equation is analyzed, many solutions are found.
– Each solution consists of a wave function that is characterized by a
particular value of E.
– A specific wave function is often called an orbital.
Quantum (wave) Mechanical Model of the Atom
• The wave function corresponding to the
lowest energy for the hydrogen atom is
called the 1S orbital
– An orbital is not a Bohr orbital (the electron is
not moving around the nucleus in a circular
orbit)
– We don’t know exactly how it is moving.
Heisenberg’s Uncertainty Principle
• There is a limitation to just how precisely
we can know both the position and
momentum of a particle at a given time.
x•(mv) > h/4
• The more accurately we know a particle’s
position, the less accurately we can know its
momentum, and vice versa.
– Limitation is too small for large particles
– Limitation is significant for small particles
Heisenberg’s Uncertainty Principle
• Applied to the electron:
– We cannot know the exact motion of the
electron as it moves around the nucleus
– Therefore, it is not appropriate to assume that
the electron is moving around the nucleus in a
well-defined orbit, as in the Bohr model.
The Physical Meaning of a Wave Function
• Meaning…What is an atomic orbital?
• The square of the function indicates the
probability of finding an electron near a
particular point in space.
[ (X1, Y1, Z1]2 = N1
• Probability Distribution: [ (X , Y , Z ]2 = N
2
2
2
2
Probability
Distribution
for the 1s
Wave
Function
Radial Probability Distribution
Quantum Numbers
•Principle Quantum Number (n):
•Angular Momentum Quantum number (l)
•Magnetic Quantum Number (ml)
•Spin Quantum Number (ms)
•(Pauli Exclusion Principle)
•See Sample Exercise 7.6
Quantum Numbers for the First Four Levels
of Orbitals in the Hydrogen Atom
Orbital Shapes and Energies
1s Orbital
Two
Representation
s of the
Hydrogen 1s,
2s, and 3s
Orbitals
2px Orbital
2py Orbital
2pz Orbital
The Boundary Surface Representations
of All Three 2p Orbitals
3d x2  y 2 Orbital
3dxy Orbital
3dxz Orbital
3dyz Orbital
3d z 2 Orbital
The Boundary Surfaces of All of
the 3d Orbitals
Representation of the 4f Orbitals in
Terms of Their Boundary Surfaces
Polyelectronic Atoms
A Comparison of the Radial Probability
Distributions of the 2s and 2p Orbitals
The Radial Probability Distribution
of the 3s Orbital
A Comparison of the Radial
Probability Distributions of the 3s,
3p, and 3d Orbitals
• Sketch a general
orbital level
diagram for atoms
other than
hydrogen.
• Explain why it
differs from
hydrogen.
Orbital Energies
Explain how you can use the periodic table to
determine the order in which orbitals fill in
polyatomic atoms.
Electron Configurations: arrangement of
electron in an atom.
•
Order of increasing energies for atomic orbitals:
•
•
•
•
Rules:
Aufbau Principle
Pauli’s Exclusion Principle
Hund’s Rule
Orbital Notation:
• Unoccupied orbital is represented by a line, with
the orbital’s name written underneath the line.
• EX: Hydrogen and Helium
Electron configuration Notation:
• Number of electron in a
sublevel is shown by adding a
superscript to the sublevel
designation.
• We can use the structure of the
periodic table to predict the
filling order of the subshells
when we write the electron
configuration of an element.
• As you move across the block
of two columns, electrons are
added to an s subshell that has a
principal quantum number
equal to the period number.
• Every time we move
across the block of six
columns we add electrons
to a p subshell that has a
principal quantum number
equal to the period
number.
• Use the periodic table to
predict the electron
configurations of Mg, Ge,
Cd,
The Orbitals Being Filled for
Elements in Various Parts of the
Periodic Table
Noble-Gas Notation:
• The first ten electrons in an
atom of each of the 3rd period
elements have the same
configuration as neon. We can
use a shorthand notation for the
electron configurations of the
third-period elements.
• Outer main energy level is fully
occupied, by eight electrons
(octet rule)
• Forth Period: Exceptions to the
Rule Lowest energy state-Most
Stable
– (College Chemistry Book)
• Chromium: [Ar] 3d54s1
• Copper:
• Silver
• Gold
• Fifth Period
• Helium – not
• Sixth and Seventh Periods
Determine the expected electron
configurations for each of the
following:
1. S
2. Ba
3. Ni2+
4. Eu
5. Ti+