# Quantum Numbers by hcj

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```									Quantum Numbers

Chemistry
March 3, 2011
Bohr Model of the Atom
• Last time we saw Hydrogen…
• Atom had a small, positive nucleus with
electrons orbiting around it.
• Hydrogen model with quantized energy
levels.
• BUT….Bohr’s model of quantized
energy levels only worked for Hydrogen,
no other atoms.
Wave Mechanical Model
• Erwin Schrodinger
• No EXACT location for the electron--”wave-
like” behavior
was able to predict the probabilities of finding
the electron at given points in space around
the nucleus.
• High probability of finding an electron in a 3-D
region called an orbital.
Energy Levels
Principal      Sublevels
• An atom has discrete      energy level   available
energy levels called:           1              1s
• Principal Energy Levels         2             2s2p
• Each principal energy
3           3s 3p 3d
level is divided into
sublevels                       4          4s 4p 4d 4f

• Each sublevel has a
specific amount of
orbitals
Orbitals
• Describes the direction in space of the
electron cloud
• Each orbital can have a maximum of 2
electrons
• S:1 orbital p:3 orbitals     d:5 orbitals
f: ? orbitals
• Orbital visuals
Orbitals
Number of   Number of      Total     Maximum
sublevels     orbitals   number of   number of
(s,p,d,f)    orbitals   electrons
1            (1)          1           2
2           (1,3)         4           8
3          (1,3,5)        9          18
4         (1,3,5,7)      16          32
Quantum Numbers
• Three dimensions Three quantum numbers
• Principal quantum number: n= 1,2,3,…
• Designates the size of the electron cloud
• Orbital quantum number: l = 0,1,2,…(n-1)
• Designates the shape of the orbital (sublevel)
• l=0(s)    l=1(p)  l=2(d)      l=3(f)
• Magnetic quantum number: ml = 0,±1 ,±2,
…,±l
• Designates the possible direction in space of the
electron cloud
Pauli’s Exclusion Principle
• Wolfgang Pauli
• Scientist (physicist) from Vienna
• Proposed 4 quantum numbers are needed to
characterize the atomic electron
• ms quantum number describes clockwise and
counterclockwise rotations of electrons in an
orbital
• The electrons in the same orbital must have
opposite spin
• ms can have values of +1/2 and -1/2 (arbitrary)
Pauli’s Exclusion Principle
• This 4th quantum number showed that:
• No two electrons in an atom can exist in
the same quantum state
• Each electron must have a different set
of quantum numbers n, l, ml, ms.
One more thing…
• Hund’s rule: electrons in an orbit shall
remain unpaired whenever possible.
• Electrons with parallel spin are more
separated in space than those that are paired
off.
• The farther the electrons are from one
another, the lower the energy of the atom.
• Less energy more stable arrangement!
• That is why we fill in orbitals one electron at a
time!

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