Download Quantum Mechanics

Quantum Mechanics
Bohr’s Model
• Bohr’s model was
better, but there were
still wholes in it.
• It didn’t do a very good
job of explaining how
ions formed.
• Bohr was able to
improve on his 1913
model, but he needed
Wolfgang Pauli to really
make sense of it.
Pauli’s Exclusion Principle
• Two objects can not be in the
same place at the same time.
• This is more or less what the
exclusion principle says.
• Stated a little more precisely, no
two fermions (e.g. electrons)
can have the same quantum
numbers.
• A set of quantum numbers is a
set of numbers that can
describe a quantum mechanical
system.
Quantum Numbers
• Principle quantum
number (n)—this tells
which electron shell
• Angular momentum
quantum number (l)—this
tells the type of sub-shell
• Azimuthal quantum
number (m)—this tells
which sub-shell
• Spin quantum number
(s)—this tells whether the
electron spins clockwise
or counter-clockwise
• n = 1, 2, 3…
• l = n-1 (0, 1, 2…)
• m = ±l (-1, 0, 1)
• s = ±½ (-½, ½)
Suborbitals
• If n = 1, then the only
possible value for m and l is 0.
• Thus, the first shell contains
only one suborbital which
holds 2 electrons.
• The suborbital is given the
symbol “s” and is spherical.
• Each additional shell begins
with an s-suborbital.
• These are shaped as nested
spheres.
Suborbitals
• For n = 2, m can equal 0 or 1.
• So, there are two types of
suborbital in the second
shell: “s” and “p”.
• For m = 1, l can equal -1, 0, or
1—this means there are 3 psuborbitals in each shell
beyond the first.
• p-suborbitals are barbellshaped and each holds 2
electrons.
• Additional p-suborbitals form
beyond those in lower shells.
Suborbitals
• For n = 3, l can equal 0, 1, or 2.
• This allows three types of
suborbital: “s”, “p”, and “d”.
• For l = 2, m can equal -2, -1, 0,
1, or 2.
• This means there are 5 dsuborbitals.
• The first 4 are shaped like the
letter “x”.
• The fifth is shape like a barbell
with a ring around it.
• In higher shells, additional dsuborbitals form outside lower
ones.
Suborbitals
• For n = 4, l can equal 0, 1, 2,
or 3.
• Shells 4 and up can support
“f” suborbitals.
• For l = 3, m can equal -3, -2,
-1, 0, 1, 2, or 3, meaning
each shell can hold 7 fsuborbitals.
• f-suborbitals have complex
shapes
• No known element has
more than one shell with fsuborbitals.