QUANTUM NUMBERS

Remember…• The Bohr atomic theory incorporated Plank’s theory of

quanta of energy• Bohr’s atomic spectra theory failed to explain the atomic

spectra for elements with multiple electrons• Scientists found that instead of the atomic spectra being

made up of 1 line, they could be made up of multiple lines

• If each line on the spectrum represented an electron dropping back to its ground state and releasing energy, where did the additional lines (electrons/energy levels) come from for elements like iron?

Hydrogen

Iron

Principal Quantum Number (n)• Bohr labelled the energy levels (a.k.a. orbits, shells) using

the letter n.

Principal quantum number: n

• n designates the main energy level of an electron in an atom

• i.e. n = 1, 2, 3, 4, etc…

Secondary Quantum Number (l)• l : secondary quantum number• Michelson theorized that within an energy level there were

different orbits/paths that an electron could take – a subshell

Secondary Quantum Number ctd.• The number of subshells in an energy level is equal to

that energy level’s value

• i.e. if n=2, then l=0, 1 (2 subshells in total)

• Ie n=3, then l = 0, 1, 2

• l = 0 (n-1)

Magnetic Quantum Number (ml)

• The magnetic quantum number (ml) indicates the direction of the electron orbit

• Explains orientation of sublevels• ml can be represented by

-l to +l

i.e.

n= 2

l can = 0, 1

If l = 1

ml = -1, 0, 1

Spin Quantum Number (ms)

• The spin quantum number indicates the direction that the electron is spinning

• Within each subshell, two electrons spin in opposite directions

• ms = -1/2 or +1/2

The Four Quantum NumbersPrincipal Quantum

Number (n)

Secondary Quantum

Number (l)

Magnetic Quantum

Number (ml)

Spin Quantum Number (ms)

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

20

-1, 0, +1 +1/2, -1/21

3

0

-2, -1, 0, +1, +2 +1/2, -1/21

2

4

0

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

+1/2, -1/21

2

3

So instead of this…

Electron distribution looks like this!