Quantum numbers

The principal quantum number, n

• 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 shell
   

• 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 subshell
• only integer values between 0 and n-1 are allowed
• sometimes called the orbital angular momentum quantum number
• spectroscopists use the following notation for subshells

 
Chemists notation for subshells.

	subshell name
0	s
1	p
2	d
3	f

• determines the orientation of orbitals within a subshell
• does not affect orbital energy (except in magnetic fields!)
• only integer values between - and + are allowed
• the number of m values within a subshell is the number of orbitals within a subshell
 

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

	possible values of m	number of orbitals in this subshell
0	0	1
1	-1, 0, +1	3
2	-2, -1, 0, +1, +2	5
3	-3, -2, -1, 0, +1, +2, +3	7

• 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

Electron Spin Identification Experiment

Silver atoms vaporized in the oven are shaped into a beam by the slit, and the beam is passed through a nonuniform magnetic field. The beam splits in two. (The beam of atoms would not experience a force if the magnetic field were uniform. The field strength must be greater in certain directions than in others.)

 |1, 1, 0 >

| 2, 0, 0 >	| 2, 1, 0 >	| 2, 1, 1 >
| 3, 0, 0 >	| 3, 1, 0 >	| 3, 1, 1 >
| 3, 2, 0 >	| 3, 2, 1 >	| 3, 2, 2 >