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Electrons and Sublevels  Electron Configurations and the Periodic Table  Writing Electron Configurations  Box and Arrow Configurations using Pauli Exclusion Principle and Hund's Rule   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

p sublevel

d sublevel

f sublevel

The spin quantum number, m_s (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

Atomic Structure Links

Electrons and Sublevels  Electron Configurations and the Periodic Table  Writing Electron Configurations  Box and Arrow Configurations using Pauli Exclusion Principle and Hund's Rule   Quantum Numbers

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