Transcript quantum mechanics

Werner Heisenberg
Werner Heisenberg proposed a theory in
1927 known as the uncertainty
principle. It argued that since we have
to use light to identify the location or
motion of an electron, the photon of
light will influence the electron's motion
and position. The uncertainty principle
says the more certain we are about a
particle's position, the less certain we
are about its momentum (mass x
velocity), and vice versa.
Louis de Broglie :if radiant energy
could, under appropriate
circumstances behave as though it
were a stream of particles, then
could matter, under appropriate
circumstances, exhibit wave-like
properties?
For example, the electron in orbit
around a nucleus. DeBroglie
suggested that the electron could
be thought of as a wave with a
characteristic wavelength.
QUANTUM NUMBERS
Variables in Schrodinger’s
equations with solutions that give
information about the probable
location of an electron.
Principle Quantum Number
1. (n) has integral values 1, 2, 3, ......
2. The principle quantum number is related to size of the
electron cloud (distance from the nucleus that the
electron is 90% of the time)
3. and energy of the orbital.
4. The larger the value of n the more time the electron
spends further from the nucleus and the higher the
energy.
n = energy level.
Angular Momentum Quantum Number
1. (l) has integral values {0 to n-1}.
2. This quantum number gives us the shape of the
probability pattern and each shape is referred to as a
sublevel. Each sublevel has a letter designation and a
numerical value.
s
0
p
1
d
2
f
3
When l = 0, the orbital is a sphere. It is
known as an “s” orbital.
When l= 1, the orbital is dumbbell shaped. The orbital
is known as a “p” orbital.
When l = 2, the orbital can exist in either of two forms. It
can be a cloverleaf pattern or a dumbbell with a donut.
In both cases, the orbital is called a “d” orbital.
When l = 3, the orbital type is called a “f ” orbital.
Magnetic Quantum Number
1. The Magnetic quantum number refers to the
possible orientations in space of each orbital.
2. (m) has integral values {-l to +l}.
3. Each different orientation of a sublevel is a
different orbital. In the p sublevel l = 1 and ml =
-1, 0, 1. Each of the values of the magnetic
quantum number represents a different p orbital
px, py, and pz. The p orbitals differ in their
orientation.
For an “s” orbital l = 0 and ml = 0
Only 1 possible orientation for “s”
orbitals. There can only be 1 “s”
orbital in any energy level.
For “p” orbitals l = 1 and ml = {-1, 0, 1}
There are 3 possible orientations for “p” orbitals. Any energy
level that ”p” orbitals occupy can have 1 to 3 “p” orbitals.
For “d” orbitals l = 2 and ml = {-2, -1, 0, 1, 2}
There can be 1 to 5 “d” orbitals in any energy levels that can have
“d” orbitals.
For “f’” orbitals l = 3 and ml = {-3, -2, -1, 0, 1, 2, 3}
An energy level that can have “f” orbitals can have
1 to 7 “f” orbitals.
Magnetic Spin Quantum Number
1. S or ms differentiates the two electrons that can exist
in a single orbital and has the value of +1/2 or -1/2.
Spin can be interpreted as the electron’s rotation
either clockwise or counter-clockwise around an
axis. A SINGLE ORBITAL CAN HOLD A
MAXIMUM OF 2 ELECTRONS.
2. Pauli’s Exclusion Principle = no two electrons in an
atom have the same set of quantum numbers.
Energy
Level
Sublevel
1
2
3
4
s
s, p
s,p,d
s, p, d, f
# e- in each
sublevel
2
2,6
2,6,10
2, 6, 10 ,14
8
16
32
Total # of e- 2
in each
energy level