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Excited Atoms
& Atomic Structure
The Quantum Mechanical
Picture of the Atom
1.
2.
Basic Postulates of Quantum Theory
Atoms and molecules can exist only in certain energy states. In each energy
state, the atom or molecule has a definite energy. When an atom or
molecule changes its energy state, it must emit or absorb just enough energy
to bring it to the new energy state (the quantum condition).
Atoms or molecules emit or absorb radiation (light) as they change their
energies. The frequency of the light emitted or absorbed is related to the
energy change by a simple equation.
E  h 
© 2006 Brooks/Cole - Thomson
hc

The Quantum Mechanical Picture of the Atom
The allowed energy states of atoms and molecules can be described by sets of
numbers called quantum numbers.
•
Quantum numbers are the solutions of the Schrodinger, Heisenberg &
Dirac equations.
Schroedinger 3-dimensional
time independent equation

(r , t )



 2  ( r , t )  V ( r , t )  ( r , t )  i
2m
t
 2
Heisenberg’s uncertainty
Equation
Dirac’s quantum
mechanical model
E. Schrodinger
1887-1961
• Four quantum numbers are necessary to describe
energy states of electrons in atoms
– n, , m, ms
© 2006 Brooks/Cole - Thomson
W. Heisenberg
1901-1976
n
1.
The principal quantum number has the symbol – n.
n = 1, 2, 3, 4, ...... “shells”
n = K, L, M, N, ......
The electron’s energy depends principally on n .
n=1
n=2
n=3
n=4
n=5
n=6
n=7
© 2006 Brooks/Cole - Thomson

2. The angular momentum quantum
number has the symbol .  tells us the shape of the orbitals
and when linked with n defines the energy of the electron
= 0  = 0, 1, 2, 3, 4, 5, .......(n-1)
= 1
=s
=p
  = s, p, d, f, g, h, .......(n-1)
n=1
n=2
n=3
=2
=d
n=4
n=5
n=6
n=7
=3
=f
© 2006 Brooks/Cole - Thomson
Quantum Numbers
3. The symbol for the magnetic quantum number is m.
m = -  , (-  + 1), (-  +2), .....0, ......., ( -2), ( -1), 
•
If  = 0 (or an s orbital), then m = 0.
– Notice that there is only 1 value of m.
This implies that there is one s orbital per n value. n  1
•
If  = 1 (or a p orbital), then m = -1,0,+1.
– There are 3 values of m.
Thus there are three p orbitals per n value. n  2
•
If  = 2 (or a d orbital), then m = -2,-1,0,+1,+2.
– There are 5 values of m.
Thus there are five d orbitals per n value. n  3
•
If  = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3.
– There are 7 values of m.
Thus there are seven f orbitals per n value, n
•
Theoretically, this series continues on to g,h,i, etc. orbitals.
– Practically speaking atoms that have been discovered or made up to this point in time only
have electrons in s, p, d, or f orbitals in their ground state configurations.
© 2006 Brooks/Cole - Thomson
Atomic Orbitals
•
•
Atomic orbitals are regions of space
where the probability of finding an
electron about an atom is highest.
s orbital properties:
• There is one s orbital per n level.
• =0
1
value of m
= 0
=s
n=1
n=2
n=3
n=4
n=5
n=6
n=7
© 2006 Brooks/Cole - Thomson
Atomic Orbitals
•
•
•
•
p orbitals are peanut or dumbbell shaped.
They are directed along the axes of a Cartesian coordinate system.
The first p orbitals appear in the n = 2 shell.
There are 3 p orbitals per n level.
– The three orbitals are named px, py, pz.
– They have an  = 1.
– m = -1,0,+1 3 values of m
© 2006 Brooks/Cole - Thomson
Atomic Orbitals
•
•
d orbital properties:
– The first d orbitals appear in the n = 3 shell.
The five d orbitals have two different shapes:
– 4 are clover leaf shaped.
– 1 is peanut shaped with a doughnut around it.
– The orbitals lie directly on the Cartesian axes or are rotated 45o from the axes.
There
–The
are 5 d orbitals per n level.
five orbitals are named
–They have an  = 2.
–m = -2,-1,0,+1,+2 5 values of m 
© 2006 Brooks/Cole - Thomson
d xy , d yz , d xz , d x 2 - y2 , d z 2
Atomic Orbitals
• d orbital shapes
© 2006 Brooks/Cole - Thomson
Atomic Orbitals
• f orbital properties:
– The first f orbitals appear in the n = 4 shell.
• The f orbitals have the most complex shapes.
• There are seven f orbitals per n level.
– The f orbitals have complicated names.
– They have an  = 3
– m = -3,-2,-1,0,+1,+2, +3
7 values of m
– The f orbitals have important effects in the lanthanide and actinide
elements.
© 2006 Brooks/Cole - Thomson
Atomic Orbitals
•
© 2006 Brooks/Cole - Thomson
f orbital shapes
Quantum Numbers
4.
–
The last quantum number is the spin quantum number which has the symbol m s.
The spin quantum number only has two possible values.
•
•
–
–
This quantum number tells us the spin and orientation of the magnetic field of the
electrons.
Wolfgang Pauli in 1925 discovered the Exclusion Principle.
•
–
–
No two electrons in an atom can have the same set of 4 quantum numbers.
Spin quantum number effects:
•
Every orbital can hold up to two electrons.
Consequence of the Pauli Exclusion Principle.
•
•
•
© 2006 Brooks/Cole - Thomson
ms = +1/2 or -1/2
ms = ± 1/2
The two electrons are designated as having
one spin up ↑ and one spin down ↓
Spin describes the direction of the electron’s magnetic fields.
E  h 
hc

 (s-1) x  (m) = c (ms-1)
Frequency times wavelength equals the speed of light
Calculate the frequency, the energy, and determine
the color of light of an excited Li+ ion emitting
radiation at 670.8nm.
 (s-1) =
E = h
© 2006 Brooks/Cole - Thomson
c (ms-1)
 (m)
The Periodic Table and
Electron Configurations
Note that the 3d subshell is higher in energy than the
4s subshell so appears in the 4th period
© 2006 Brooks/Cole - Thomson
Quantum Numbers
The principal quantum number has the symbol ~ n
which defines the energy of the shell
n = 1, 2, 3, 4, ...... “shells”
The angular momentum quantum number has the symbol ~  which
defines the subshells.
 = 0, 1, 2, 3, 4, 5, .......(n-1)
 = s, p, d, f, g, h, .......(n-1)
n and  define the energy of the electron
The symbol for the magnetic quantum number is m which defines the
orbital.
m = -  , (-  + 1), (-  +2), .....0, ......., ( -2), ( -1), 
The last quantum number is the spin quantum number which has the symbol ms which
characterizes the single electron.
The spin quantum number only has two possible values.
ms = +1/2 or -1/2
one spin up ↑ and one spin down ↓
© 2006 Brooks/Cole - Thomson
The Nucleus:
Build by adding the required number of protons
(the atomic number) and neutrons (the mass of the atom)
Electrons:
Hund’s Rule states that each orbital will be filled singly
before pairing begins. The singly filled orbitals will have
a parallel spin.
Pauli’s Exclusion Principle states that paired
electrons in an orbital will have opposite spins.
Fill the electrons in starting with the lowest energy level adhering to
Hund’s and Pauli’s rules.
Neon © 2006 Brooks/Cole - Thomson
The Periodic Table and Electron Configurations
•
•
Now we can write a complete set of quantum numbers for all of the electrons in these
three elements as examples.
– Na
First for 11Na.
– When completed there must be one set of 4 quantum numbers for each of the 11
electrons in Na (remember Ne has 10 electrons)
3s
11 Na
Ne
3p
Ne 3s1

[Ne] = 1s22s22p6
© 2006 Brooks/Cole - Thomson
Configurat ion
The Periodic Table and
Electron Configurations
11Na
1s22s22p63s1
© 2006 Brooks/Cole - Thomson
n

m
1
0
0
2 nd e - 1
0
0
3rd e -
2
0
0
4 th e -
2
0
0
5th e -
2
1
-1
6 th e -
2
1
0
7 th e -
2
1
1
8 th e -
2
1
1
9 th e -
2
1
0
10 th e -
2
1
1
11th e -
3
0
0
1st e -
ms
 1/2 
1 s electrons
 1/2 
 1/2 
2 s electrons
 1/2 
 1/2 

 1/2 
 1/2 

2 p electrons
 1/2 
 1/2 

 1/2 

 1/23 s electron
The Periodic Table and Electron Configurations
•
26Fe.
•
– We should have one set of 4 quantum numbers for each of the 26 electrons in Fe.
To save time and space, we use the symbol [Ar] to represent the first 18 electrons in Fe
3d
26 Fe
s
Ar   
4s
  
4p
Configurat ion
Ar  4s2 3d6

n

m
[Ar] 19 th e -
4
0
0
20 th e -
4
0
0
ms
21st e -
3
2
-2
 1/2 

4 s electrons
 1/2 

 1/2
22 nd e -
3
2
-1
 1/2
23rd e -
3
2
0
 1/2
24 th e -
3
2
1
 1/2
25 th e -
3
2
2
 1/2
26 th e -
3
2
-2
 1/2


3d electrons

1/2 

1/2
© 2006 Brooks/Cole - Thomson
© 2006 Brooks/Cole - Thomson
© 2006 Brooks/Cole - Thomson
© 2006 Brooks/Cole - Thomson
Electron Affinities of Some Elements
Electron Affinity (kJ/mol)
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
0
-50
-100
-150
-200
-250
-300
-350
-400
Atomic Number
© 2006 Brooks/Cole - Thomson
© 2006 Brooks/Cole - Thomson
Electronegativity
Increases
Increases
© 2006 Brooks/Cole - Thomson