The Quantum Model of the Atom
Mrs. Johnson
de Broglie
• Light behaves as both a wave and a particle
• So do eˉ ( they are particles, but also have
wave like properties because they can be
bent, or diffracted)
Bohr vs. the Quantum Model
• In each energy level, a certain amount of
electrons can fit
• 2n2
• When n=1, there are 2 electrons
• When n=2, there are 8 electrons
• When n=3, there are 18 electrons
• When n=4, there are 32 electrons
Electrons
• Electrons do not travel around the nucleus
in neat orbits, said by Bohr
• They exist in certain regions called orbitals
• Orbital-3 dimensional region around the
nucleus that indicates the probable location
of an eˉ
• Energy of eˉ are higher when further from
nucleus
Uncertainty Principle
• Can confine an eˉ to a specific energy level
(quanta) or region of an atom
• It mathematically isolates an eˉ to a specific
orbital, but cannot tell its exact position
• Schrodinger’s equation allows physicists to
find the probable location of an eˉ
Quantum Numbers
• Specify the properties of atomic orbitals and
the properties of e‾ in orbitals
• 1st three quantum #’s: indicate the main
energy level, the shape and the orientation
of an orbital
• 4th #: spin #- describes a fundamental state
of the eˉ that occupies the orbital
Principle Quantum #-n
• Indicates the main energy level occupied by
the eˉ
• n-positive integers- 1,2,3…
• As n increases, the eˉ’s energy and its av.
distance from the nucleus increases
• n=1, occupies the 1st or lowest main energy
level and is located closest to the nucleus
n
• More than one eˉ can have the same n value
• These eˉ’s are sometimes said to be in the
same eˉ shell or main energy level
• When n=1, 2 e can fit
• When n=2, 8 e can fit
• How many e will fit when n=3 and n=4?
• Answers: 18, 32
On your own
• What is the value of n for electron in H?
What is the value of n for the last e in Cl?
What is the value of n for the last e in Cu?
Answers: n=1, n=3, n=4
Angular Momentum Quantum #-l
• Indicates shape of orbital
• Sublevels: orbitals of different shapes
• Sublevels exist for a given value of n except
for the 1st main energy level
• The # of orbital shapes possible=n
• l= 0 and all possible integers less than or
equal to n-1
Examples
•
•
•
•
•
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When n=2
How many shapes are there?
Answer: 2
What is l equal to?
n-1 or (2-1)
So l= 1 and l =0
Orbital Letter Designations for
values of l
0
s
1
p
2
d
3
f
Sublevels
•
•
•
•
s-spherical
p-have dumbbell shapes
d-more complex
f- too complex
Try This
• When n=1, how many orbitals does it have,
what is the value for l and which sublevel is
it in?
• When n=2?
• When n=3?
• When n=4?
Answers
• When n=1, there is only 1 orbital, l=0 and it
is only in the s sublevel
• When n=2, there are 2 possible orbitals, l=0
and 1, and it is in the s and p sublevels
• When n=3, there are 3 possible orbitals, l=0,
1 and 2, and it is in s, p,and d sublevels
• When n=4, there are 4 possible orbitals,
l=0,1,2 and 3, s,p,d,f sublevels
Magnetic Quantum #-ml
• Indicates the # of orbitals per
sublevel(orientations)
• Atomic orbitals can have the same shape,
but different orientations around the nucleus
• When l=0, m=0
• When l=1, m=-1,m=0,m=1(3 orientations)
• When l=2, m=-2,m=-1,m=0,m=1,m=2
(5 orientations)
Spin Quantum # ms
• An e in an orbital can be thought of as
spinning on an internal axis
• It spins in 1 of 2 possible directions or states
• As it spins, it creates a negative field
• 2 possible values +1/2 and –1/2
• A single orientation can hold a maximum of
2 e which must have opposite signs
Electron Configuration
• The arrangement of e in an atom
• Each atom of each element has its own
• e arrange themselves so that they have the
lowest possible energies
• The lowest–energy arrangement of the e’s is
called the element’s ground-state config.
• There are rules that allow us to determine
these ground-state configurations
Aufbau
st
Principle-1
Rule
• Shows the order in which e’s occupy
orbitals
• An e occupies the lowest-energy orbital that
can receive it
• Figure 11.32 (atomic orbitals in order of
increasing energy)
• Which orbital has the lowest energy? What
about the next lowest energy?
Aufbau con’t
• What looks strange about the order as
energy increases?
• Beginning with n=3, the energies of the
sublevels in different main energy levels
begin to overlap
• The 4s sublevel is lower in energy than the
3d sublevel, so the 4s orbital is filled before
any e’s enter the 3d orbitals
Why?
• Less energy is required for 2 e’s to pair up
in the 4s orbital than for a single e to
occupy a 3d orbital
• What sublevel is filled next after 3d?
• Pauli Exclusion Principle-no two e’s in the
same atom can have the same set of
quantum #’s ( 3 are the same)
Pauli Exclusion Principle
• 2 e’s can occupy the same orbital, but must
have opposite spins
• Each arrow represents 1 of the atoms 2 e’s
• The direction of the arrow represents the e’s
spin
Hund’s Rule
• Orbitals of equal energy are each occupied by 1 e
before any orbital is occupied by a 2nd e
• All e’s in singly occupied orbitals must have the
same spin
• e-e repulsion is minimized so e arrangements can
have the lowest energy possible
• What is the max # of unpaired e’s in a d sublevel?
Representing e configurations
• 3 notations
1)orbital notation
2)e configuration notation
3)noble-gas notation
Orbital Notation
_____=unoccupied orbital
Orbital’s name is written below the line n&l