Transcript Chapter 7 - Gordon State College

Chapters 7 & 8
Quantum Mechanical
Model; Electronic Structure
of the Atoms & Periodic
Trends
Definitions
• Atoms - smallest particles of
matter
• Matter - has mass, volume and
specific position
• Energy - no mass; a wave
function; delocalized
Einstein’s Contribution
• Energy is related to mass as
seen in the equation:
E = mc2
Law of Conservation of Energy
• Energy can never be
destroyed. It can only be
converted from one form to
another.
Forms of Energy
• Electromagnetic radiation
wavelength, frequency and speed
• Light
• Heat
Electromagnetic Spectrum
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Radio Waves
Microwaves, Radar Rays
Infrared
Visible
UV
X-rays
Gamma Rays
The Wave Nature of Light
The Wave Nature of Light
Chemistry in Color
• Specific elements gave color
when heated in flame.
• Continuous spectrum - e.g.,
rainbow
• Line Spectrum
Line Spectra
• Held the key to the structure
of the atom!
The Bohr Atom
• Bohr:
suggested that electrons were
responsible for the line
spectra.
Proposed that electrons
traveled around the nucleus of
the atom in shells
The Bohr Atom
• Bohr:
associated each shell w/ a particular
energy level. The farther away, the
higher the Energy.
Allowed electrons to jump from one
shell to another. (ground state
excited state)
Comparison
• Bohr Model similar to model for
solar system where the planets
revolve in their particular orbits.
• Difference: Electrons can jump
from one shell to another. The
planets do not!
Ionization
• An electron can absorb so
much energy that it can jump
completely from the atom!
Quantized Energy and
Photons
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The Photoelectric Effect and Photons
If light shines on the surface of a metal, there is a
point at which electrons are ejected from the metal.
The electrons will only be ejected once the threshold
frequency is reached.
Below the threshold frequency, no electrons are
ejected.
Above the threshold frequency, the number of
electrons ejected depend on the intensity of the light.
Matter and Energy
• Matter and Energy are not distinct!
• Proof: Matter can absorb or emit
energy.
• Max Planck’s Postulate: Energy can be
gained or lost only in whole numbers or
integer multiples, hn.
Wrong assumption
• Matter was assumed to
transfer any amount of
energy because E was
continuous.
Quantum
• E can be quantized or
delivered in small packets of
size hn, called a Quantum.
• Quanta = photon
Quantum Mechanical Model
• De Broglie and Schroedinger
• Corrected Bohr’s model
• determined that E had wave
properties and mass
Quantum Mechanical Model
• re-evaluated electron as
occupying volume of space
instead of shells that were like
orbits.
• Orbital - volume of space
occupied by an electron
Quantum Mechanics and
Atomic Orbitals
If we solve the Schrödinger
equation, we get wave functions
and energies for the wave
functions.
• We call wave functions orbitals.
• Orbitals were located in levels.
Quantum Mechanical Model
• De Broglie and Schroedinger
• Corrected Bohr’s model
• determined that E had wave
properties and mass
Quantum Mechanical Model
• re-evaluated electron as
occupying volume of space
instead of shells that were like
orbits.
• Orbital - volume of space
occupied by an electron
Quantum Mechanics and
Atomic Orbitals
If we solve the Schrödinger
equation, we get wave functions
and energies for the wave
functions.
• We call wave functions orbitals.
Principal Quantum Number, n
• Schrödinger’s equation requires 3
quantum numbers:
1.Principal Quantum Number, n.
This is the same as Bohr’s n. As n
becomes larger, the atom becomes
larger and the electron is further
from the nucleus. N refers to the
shell.
Azimuthal Quantum Number, l.
2. This quantum number depends
on the value of n. The values of l
begin at 0 and increase to (n - 1).
We usually use letters for l (s, p, d
and f for l = 0, 1, 2, and 3).
Usually we refer to the s, p, d and
f-orbitals.
Representations of
Orbitals
Magnetic Quantum Number, ml.
3. This quantum number
depends on l. The magnetic
quantum number has integral
values between -l and +l.
Magnetic quantum numbers
give the 3D orientation of
each orbital.
Representations of
Orbitals
The s-Orbitals
Shape of Orbitals
• s - sphere
• p - dumbbell
•d -
double dumbbell
Representations of
Orbitals
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The p-Orbitals
There are three p-orbitals px, py, and pz.
The three p-orbitals lie along the x-, y- and z- axes of
a Cartesian system.
The letters correspond to allowed values of ml of -1,
0, and +1.
The orbitals are dumbbell shaped.
As n increases, the p-orbitals get larger.
All p-orbitals have a node at the nucleus.
Representations of
Orbitals
The p-Orbitals
Representations of
Orbitals
The d and f-Orbitals
• There are five d and seven f-orbitals.
• Three of the d-orbitals lie in a plane
bisecting the x-, y- and z-axes.
• Two of the d-orbitals lie in a plane
aligned along the x-, y- and z-axes.
• Four of the d-orbitals have four lobes
each.
• One d-orbital has two lobes and a collar.
Pauli Exclusion Principle
• An orbital can only hold 2
electrons and they must have
opposite spins!
• Example: px, py, pz
Rules for Occupancy and
Pairing
• Opposite spins pair up.
• Hund’s Rule:
For the same sublevel, each
orbital must be occupied singly
before pairing can occur. This is the
lowest E for an atom configuration.
Heisenberg Uncertainty
Principle
• “There is a fundamental limitation
as to how precisely we can determine
the position and momentum of a
particle at a given time.”
• 90-95% probability of finding the
electron in the orbital
Magnetic Spin Quantum Number, ms
• Gives insight into the spin of the electron
• 2 Possible Values: ½ and – ½
Many-Electron Atoms
Orbitals and Their Energies
• Orbitals of the same energy are said to be
degenerate.
• For n  2, the s- and p-orbitals are no
longer degenerate because the electrons
interact with each other.
• Therefore, the Aufbau diagram looks
slightly different for many-electron
systems.
Energy Levels
• The electrons are found at a certain
distance from nucleus in their
shell(s).
• energy level = shell (interchangeable
terms)
• Electrons in the same shell have the
same E.
Heisenberg Uncertainty
Principle
• “There is a fundamental limitation
as to how precisely we can determine
the position and momentum of a
particle at a given time.”
• 90-95% probability of finding the
electron in the orbital
Shorthand Notation
• Uses the closest noble gas before the given
element to represent the inner electrons.
• Al = 13 electrons 1s2 2s2 2p6 3s2 3p1
• Shorthand Notation: [Ne] 3s2 3p1
–
Neon represents the 10 inner electrons
Periodicity
• Valence electrons determined
the position of the atoms in
the periodic table and
predicted the reactivity of the
elements.
Periodic Table
• Organized according to
Electronic Configuration of
elements
• Based on the Aufbau Principle of
building up the number of
electrons and protons
Definitions
• Core Electrons - inner
electrons
• Valence Electrons - electrons
on the outermost energy level
of an atom
Valence Electrons
• Are the electrons in the outermost shell
• Determines the group where the element
belongs in the periodic table.
• For ex., 1s22s22p3 = element belongs to Grp V.
Outermost level is 2. Add the electrons in 2s
and 2p orbitals.
Sample Problem
• What is the largest principal
quantum number in the ground state
electron configuration of iodine ?
Sample Problem
• What is the azimuthal quantum
number for the orbitals being filled
in the Lanthanide series?
Sample Problem
• What is the azimuthal quantum
number for the orbitals being filled
in Group II?
Sample Problem
• What is the azimuthal quantum
number for the orbitals being filled
in Group VII?
Sample Problem
• 1. How many electrons have quantum
numbers 4,2,1,-1/2.
• 2. How many orientations have n=5 and
l=2?
• 3. How many electrons have n=5 and l=2?
Transition Metals
• Electron configuration of transition metals
differ from that of regular A-block elements.
• Preference for half-filled and totally filled dorbitals.
• Transition metals do not like the d4 and d9
configuration. They borrow one electron from
the closest s orbital (before the d orbital) to
make d5 or d10.
• Lanthanides and Actinides do not
like ending the electron
configuration in f6 and f13. They
borrow one electron from the
closest s orbital (before the f
orbital) to make f7 or f14.
Sample Problem
• Write the electronic configuration of
Molybdenum?
• Write the abbreviated electronic
configuration of Molybdenum.
Trends
• Atomic Size
• Ionization Energy
• Electron Affinity
Sample Problem
• Arrange the following in
order of increasing atomic
radii.
• A.) Ba, Sr, S, Pb, V
• B.) Au, Cd, Tl, In, Te
Sample Problem
• Arrange the following
elements in order of
increasing ionization energies.
• A.]
• B.]
Ca, Mg, F, B, Br
Kr, O, Se, Tl, Na
General Trend
• As you go across the periodic table,
electron affinity increases.
• As you go down the periodic table,
electron affinity decreases. (too far
away for nucleus to have much of an
effect)
Sample Problem
• Arrange the following in
order of increasing electron
affinity.
• Ba, Sn, C, Pd, Fe