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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