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Name___________________________________________________
QUANTUM MECHANICAL MODEL OF THE ATOM
Contributors to the quantum mechanical model in mid-1920s:
Louis deBroglie
Erwin Schrödinger
Werner Heisenberg
Schrödinger – treat e– as a wave
Schrödinger equation: Ĥ = E
solve to get wave functions, which predict locations of electrons
wave function = ORBITAL – region with 90% probability of holding an e–
QUANTUM NUMBERS
orbitals characterized by 4 no.’s:
1. principal quantum number (n)
value of n corresponds to:
o
n=
o
2. angular momentum quantum # (l)
l = 0, 1, … n-1 (l ≠ n)
If n = 1 then l =
If n = 2 then l =
If n = 3 then l =
value tells you:
assign a letter:
l =0
1
2
3
shapes: pages 311 – 313
___ ___ ___ ___
put first 2 quantum numbers together:
n = 1, l = 0
_____
n = 4, l = 2
_____
n = 3, l = 1
_____
3s
_______________
5f
_______________
3. magnetic quantum number (ml)
ml = -l to +l including zero
values of ml tell you:
If l = 0 then ml =
o
If l = 1 then ml =
o
If l = 2 then ml =
4. spin quantum # (ms)
ms = + ½ or – ½
value gives:
A maximum of ____ e– fit in each orbital!
PAULI EXCLUSION PRINCIPLE
In a given atom, no two electrons can have four identical quantum numbers.
Complete the chart below:
n
l
orbitals
# orbitals
# e–
List 4 possible quantum numbers for the following using the notation (n, l, ml, ms):
an e– in a 2s orbital
an e– in a 3p orbital
an e– in a 4d orbital