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Modern Atomic Theory
The Bohr Atom
Neils Bohr proposed a
model of the atom that
explained a wide variety
of phenomena that were
puzzling scientists in the
late 19th century.
His model began the
basis for the field of
quantum mechanics .
Neils Bohr (1915)
In the Bohr model, electrons orbit the nucleus of an
atom.
Unlike earlier planetary models the Bohr atom has
limited of fixed orbits that are available to electrons
Under the right circumstances an electron can go
from its ‘grounds state’ (lowest energy orbit) to a
higher (excited) state or it can decay from a higher
state to a lower state, but it cannot remain between
these states.
The allowed energy states are called “quantum” states
and are referred to by the principal “quantum numbers
“ 1, 2, 3, etc.
For an electron to jump
to a higher quantum
state, the atom must
receive energy from the
outside world
(electromagnetic
radiation)
When an electron drops from
a higher state to a lower state
the atom must give off energy
(electromagnetic radiation).
For an atom to absorb light (i.e. for the light
energy to cause an electron to move from a lower
energy state En to a higher energy state Em, the
energy of a single photon must equal , almost
exactly, the energy difference between the two
states.
∆E = Em − En
hc
λ=
∆E
Is light a wave or a particle?
Light has the characteristics of both a wave and a
particle. Light is made up of particles called
“photons”
…following Einstein's introduction
of photons in light waves, one
knew that light contains particles
which are concentrations of
energy incorporated into the
wave, suggests that all particles,
like the electron, must be
transported by a wave into which
it is incorporated…
Louis Victor deBroglie
deBroglie’s Postulate
or the “Particle-Wave Duality Theory”
"With every particle of matter with mass m and
velocity v a real wave must be 'associated', related to
the momentum by the equation
h
h
v2
λ= =
1− 2
p mv
c
Where:
λ=
h
mv
λ= wavelength (m)
h = Planck’s constant (Js)
m = rest mass (kg)
v = velocity (m/s)
Practice
1. Using Einstein’s equation E = mc2 and Planck’s equation
E = hν derive deBroglies Postulate
2. Compare the velocity of an electron (mass = 9.11 x 10-28g)
and a neutron (mass = 1.67 x 10-24 g), both with deBroglie
wavelengths of 0.100 nm (1 J = 1 kg m2/s2).
3. A golf ball weighs about 0.100 lb. Calculate the deBroglie
wavelength of a golf ball traveling at 1.00 x 102 miles per
hour.
4. Calculate the mass of a shotgun pellet travelling at 150 m/s
with a deBroglie wavelength of 3.7 x 1024nm
Wave Mechanical Model
Werner Heisenberg elucidated the
Uncertainty Principle (1923)
Classical physics had always
assumed that precise location and
velocity of objects was always
possible.
Heisenberg discovered that this
was not necessarily the case at the
atomic level. In particular, he stated
that the act of observation
interfered with the location and
velocity of small particles
Wave Mechanical Model
Heisenberg Uncertainty
Principle
There is a fundamental
limitation to just how
precisely we can know
both the position and
momentum of a particle
at a given time
Wave Mechanical Model
Erwin Schrodinger developed
the equation which is used today
to understand atoms and
molecules - the Schrodinger
Equation (1926)
Erwin Schrodinger took the
ideas developed by de Broglie,
Heisenberg and others and put
them together in a single
equation that is named after
him. Solving this equation can in
principle predict the properties
and reactivities of all atoms and
molecules.
Quantum Theory
Orbitals and energies are the central
objects that determine the properties of
atoms and molecules in the Quantum
Theory
Although the Schrodinger equation is too
difficult to solve for any but the simplest
atoms/molecules, we can nevertheless
extract some essential conclusion from it:
Energies are quantized
Atoms and molecules cannot have any
energy but only certain ‘discrete’ energies.
This means that energies are ‘quantizied’.
The orbitals, associated with each energy level and sub-level,
determine where the electrons are located.
Just what is an
orbital?
An orbital is a specific
wave function, a
function of the
coordinates x, y, and
z. In other words
‘position’ Each wave
function has a
particular value of E,
energy, associated
with it.
S Orbitals
Orbitals are definitely not Bohr orbits. They are
electron clouds characterized by values for n, l, ml,
and, ms. Quantum mechanics describes them as
regions (energy levels) of high probability for finding
an electron.
P Orbitals
Each orbital is characterized by 4 quantum numbers:
n = principal, 1,2,3, …. (size)
l = angular momentum, l=0 (s(s-orbital), l=1 (p(p-orbital),
l=2 (d(d-orbital), l=3 (f(f-orbital) etc. (shape)
ml = magnetic, orientation in space,
l, …, +1, 0, -1, …, -l
ms = spin, electrons’
electrons’s spin, +1/2 or -1/2
We can use the analogy of ‘houses’ to help us
understand the quantum numbers
Quantum Numbers
Quantum Numbers
Quantum Numbers
Assigning quantum numbers to the 3p1 electron of
aluminum
3, 1, +1, +1/2
n l ml ms
http://www.chem.ufl.edu/~itl/2045/matter/TB06_002.GIF
Rules
The Aufbau Principle states that energy levels must be
filled from the lowest to the highest and you may not
move on to the next level unless the previous level is
full. Use the periodic table as a guide
Pauli Exclusion Principle states that no two electrons
(fermions) in an atom can have identical quantum
numbers.
numbers. Only two electrons may occupy any one
orbital and they must have opposite spins
Hund’s Rule: every orbital in a subshell is singly
occupied with one electron before any one orbital is
doubly occupied, and all electrons in singly occupied
orbitals have the same spin
Rules
Exceptions to the rules
There are a few exceptions to the rules listed
above when filling electron configurations. A
halfhalf-full “s” orbital and a “d” subshell with 5 or 10
is more stable than following the Aufbau
Principle.
Cr, Mo, W: s1 d5
Cu, Ag, Au: s1 d10
Electron Configurations
Orbital information is often described in a
notation called an electron configuration
1s22s22p3
Electron Configurations
Shows the number of
electrons in the orbital
Represents the
principal energy level
1s2
Indicates the shape of
the orbital
Orbital Diagrams
This information is also described using orbital
diagrams. Arrows are added to an orbital
diagram to show the distribution of electrons in
the possible orbitals and the relative spin of
each electron
_↑↓_
↑↓_
1s
_↑↓_
↑↓_
2s
_↑ _ _↑ _ _↑ _
2p
Writing Electron Configurations
Determine the number of electrons in the atom from its
atomic number
Following the rules, add electrons to the sublevels in
correct order of filling
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d,
5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p
s = 2, p = 6, d = 10, f =14
To check your complete electron
configuration, look to see whether
the location of the last electron
added corresponds to the
element’s position on the periodic
table
Drawing Orbital Diagrams
Draw a line for each orbital of each sublevel
mentioned in the complete electron configuration.
Draw one line for each s sublevel, three for each p
sublevel, 5 for each d sublevel and 7 for each f
sublevel.
_↑↓_
↑↓_
1s
For orbitals containing two electrons, draw one
arrow up and one arrow down to indicate the
electrons’ opposite spins.
Label each sublevel