QUANTUM NUMBERS

four

In quantum theory, each electron in an atom is assigned a set of _ quantum numbers.

location

Three of these nubers give _ the of the electron

orientation

fourth number gives the _ of the electron within the orbital

quantum numbers

n, l, m_l, m_s

n

principal quantum number

1, 2, 3, 4, ….

n =

principal quantum number n

distance of e^- from the nucleus

l

angular momentum quantum number

0, 1, 2, 3, … n-1

for a given value of n, l =

0

s orbital l=

1

p orbital

2

d orbital

3

f orbital

angular momentum quantum number l

Shape of the “volume” of space that the e^- occupies

m_l

magnetic quantum number

-l, …., 0, …. +l

for a given value of l

m_l =

m_l = -1, 0, or 1

if l = 1 (p orbital)

m_l = -2, -1, 0, 1, or 2

if l = 2 (d orbital)

magnetic quantum number m_l

orientation of the orbital in space

m_s

spin quantum number

+½ or -½

m_s =

spin quantum number m_s

describes the intrinsic angular momentum or spin of an electron or other particle, which can be either clockwise or anticlockwise

Pauli exclusion principle

no two electrons in an atoms can have the same four quantum numbers.

y

Existence (and energy) of electron in atom is described by its unique wave function

Shell

electrons with the same value of n

Subshell

electrons with the same values of n and l

Orbital

electrons with the same values of n, l, and m_l

2

How many electrons can an orbital hold?

n and l

Energy depends on

Aufbau principle

“Fill up” electrons in lowest energy orbitals

Hund’s rule

The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

Order of orbitals (filling) in multi-electron atom