Quantum Numbers by hcj


									Quantum Numbers

   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
• 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
• Instead, Schrodinger’s mathematical equation
  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
• Describes the direction in space of the
  electron cloud
• Each orbital can have a maximum of 2
• S:1 orbital p:3 orbitals     d:5 orbitals
     f: ? orbitals
• Orbital visuals
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,
  • 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
• 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
• 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

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