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Quantum Numbers

The 4 quantum numbers are the address of an electron.

Quantum numbers

Think of the quantum numbers as addresses for electrons

The principal quantum number, n    (the energy level)

    • determines the size of an orbital (larger n = bigger orbitals)

    • largely determines the energy of the orbital (larger n = higher energy)

    • can take on integer values n = 1, 2, 3, ..., 

    • all electrons in an atom with the same value of n are said to belong to the same principle energy level
       

the azimuthal quantum number,      (the sublevel)

    • designates the overall shape of the orbital within a shell

    • affects orbital energies (larger  = higher energy)

    • all electrons in an atom with the same value of  are said to belong to the same sublevels

    • only integer values between 0 and n-1 are allowed

    • sometimes called the orbital angular momentum quantum number

    • spectroscopists use the following notation for sublevels

       
      Chemists notation for sublevels.

       

      sublevel name

      0

      s

      1

      p

      2

      d

      3

      f
       

the magnetic quantum number, m   (the orbital (box) the electron is in)

    • determines the orientation of orbitals within a sublevel.

    • does not affect orbital energy (except in magnetic fields!)

    • only integer values between - and + are allowed

    • the number of m values within a sublevel is the number of orbitals within a sublevel

        The number of possible m values determines the number of orbitals in a sublevel.

      **note the middle orbital is ZERO

       

      possible values of m

      number of orbitals in this sublevel

      0

      0

      1

      1

      -1, 0, +1

      3

      2

      -2, -1, 0, +1, +2

      5

      3

      -3, -2, -1, 0, +1, +2, +3

      7

 s sublevel

0

p sublevel

- 1 0 +1

d sublevel

-2 -1 0 +1 +2

f sublevel

-3 -2 -1 0 +1 +2 +3

The spin quantum number, ms (the direction of the arrow)

    • several experimental observations can be explained by treating the electron as though it were spinning

    • spin makes the electron behave like a tiny magnet

    • spin can be clockwise or counterclockwise

    • spin quantum number can have values of +1/2 or -1/2 (arrow up or arrow down)

Examples The 4 quantum numbers of the last electron in each sublevel shown below


2p

2p4  n =2 =1

m =-1

 ms =-1/2

5d
5d5  n =5 =2

m =+2

 ms =+1/2

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