Download Quatum Mechanics 2

Quantum Mechanics
Through the Looking Glass
This is how the model of the atom has
developed so far:
Rutherford
Bohr-Planetary Model
Correcting Bohr’s Planetary Model
…using the Photoelectric Effect
Louis DeBroglie’s insight:
If light radiation can have a particle nature
then why can’t particles have a wavelike nature?
If electrons are particles
Electrons must have a wavelike nature
 =
h
mv
Werner Heisenberg (1901-1976)
Heisenberg’s Uncertainty Principle
There is an uncertainty in either the position or
the momentum of an electron that cannot be
reduced beyond a certain minimum level
Is Shrodinger’s cat dead or alive?
The Quantum Mechanical Model
Describes the wave properties of electrons
and regions of space surrounding the nucleus
Called orbitals
Where there is a high probability of
finding electrons
Describing an electron’s address
Bohr’s model places the electron in
a quantum energy level (n)
Bohr-Planetary Model
Describing an electron’s address
using the Quantum Mechanical Model
Electrons exist in orbitals
A collection of orbitals with the same energy
is called an electron shell designated (n)
1st quantum #-principle quantum number (n)
n = (1,2,3,…, ) describes shell or energy level
Describing an electron’s address
using the Quantum Mechanical Model
2nd quantum # - azimuthal number (l), value
0 to n-1 describes sublevel
3rd quantum # - magnetic number (ml), value =
l to 0 to-l The orientation of the orbital in space
4th Quatum # - Spin (ms), value is + or – ½,
describes the spin
The first energy level (n = 1) is constructed from
a single orbital (l = 0), also designated ‘1s’,
which is spherical ( ml = 0)
The second energy level (n = 2) is constructed from
a single orbital (l = 0) also designated ‘2s’
which is spherical ( ml = 0)
The third energy level (n = 3) is constructed from
a single orbital (l = 0) also designated ‘3s’
which is spherical ( ml = 0)
Energy level ‘n = 2’ is more complex than energy
level ‘n =1’ and is constructed from
two kinds of orbitals
The innermost part of ‘n =2’ consists of a
single spherical orbital designated ‘2s’
The outermost part of ‘n = 2’ consists of
three orbitals which are not spherical, (l = 1)
Each dumbbell-shaped orbital (l = 1), also
designated ‘2px, 2py,2pz’is oriented along
the x, y, and z axes ( ml = -1, 0, 1)
Like the ‘s’ orbital, the ‘p’ orbitals also repeat
in subsequent energy levels
Energy level ‘n = 3’ is more complex than energy
level ‘n =1’ or ‘n = 2’ and consists of an
innermost spherical orbital designated ‘3s’
The middle part of ‘n = 3’ consists of
three dumbbell-shaped orbitals , (l = 1)
The outermost part of ‘n = 3’ consists of
five orbitals which are also not spherical, (l = 2)
Each four-lobed orbital (l = 2), also designated
‘3 d orbital ’is oriented along different
planes ( ml = -2, -1, 0, 1, 2)
Like the ‘s’ and ‘p’ orbitals, the ‘d’ orbitals also
repeat in subsequent energy levels
Energy level ‘n = 4’ is more complex than energy
level ‘n =1, 2, or 3’ and consists of an
innermost spherical orbital designated ‘4s’
The lower middle part of ‘n = 4’ consists of
three dumbbell-shaped orbitals , (l = 1)
The upper middle part of ‘n = 4’ consists of
five orbitals which are also not spherical, (l = 2)
The outermost part of ‘n = 4’ consists of seven
orbitals, also designated ‘f ’ orbitals,
which are also not spherical, (l = 3)
In fact, they are a real nightmare
( ml = -3, -2, -1, 0, 1, 2, 3)
Describing an electron’s address
Quantum Mechanics: Where ever you go...
there you are!
Schwartzchild’s Radical
which of the following is not an allowable
quantum number
1. 4,4,3,1/2
2. 3,2,2,1
3. 5,2,-1,-1/2
What are the maximum number of
electrons allowed that have the quantum
numbers designated?




1. n=3
2. n=3, l=2
3. n= 3, l=2, ml = 1
4. n= 3, l=2, ml = 1, ms = 1/2
Which of the following are in an excited
state and what element do they represent?
 1. 1s22s22p63p64s23d104p65s24d105p6
How many unpaired electrons are in
each of the following.
 Cr
 Fe3+
 Cl1-