QUANTUM MECHANICS

NEILS BOHR

HELIUM ATOM

+N

N

+-

-

proton

electron

neutron

Shell

3 p+

4 n02e– 1e–

Li shorthand

Bohr - Rutherford diagrams

2 p+

2 n0

He

3 p+

4 n0

Li

11 p+12 n°

2e– 8e– 1e–

Na

8 p+8 n°

2e– 6e–

O

4 p+5 n°

Be

5 p+6 n°

B

13 p+14 n°

Al

LOUIS de BROGLIE - 1924

• He proposed that electron behaves like a wave, specifically a standing wave. A standing wave is a wave that does not travel down its medium.

• A standing wave is obtained when one point (called the node) in the middle of the wave is stationary.

WERNER HEISENBERG - 1927

• UNCERTAINTY PRINCIPLE• States that there is NO way to determine

both the precise location and momentum (mass X velocity) of small particles at the same time.

• Principle implies that if we could measure the momentum of an electron accurately, we could NOT determine its location at the same time.

QUANTUM•values used to

express the “quanta” or

the packets of energy

SCHRODINGER – 1926

QUANTUM MECHANICS

•“wave mechanics” is a

field that described the

behavior, as well as the energies,

of particles.

QUANTUM NUMBERS

QUANTUM NUMBERS

• principal quantum number

• orbital quantum number

• magnetic quantum number

• electron spin quantum number

PRINCIPAL QUANTUM NUMBER (n)

• Corresponds to the

energy level numbers. As (n) increases, the average distance of an electron from the nucleus also increases.

• The larger the (n) the larger the atomic orbital.

+N

N

+

n=1n=2n=3

n= so on…

K L M

ORBITAL QUANTUM NUMBER (l)

• AZIMUTHAL

• The sublevels that describes the shape of the atomic orbitals.

• Examples: l = 0 s orbital

l = 1 p orbitall = 0 d orbital

l = 1 f orbital

+N

N

+

n=1n=2n=3

n= so on…

K L M

POSSIBLE ANGULAR MOMENTUM QUANTUM

NUMBERS (l)PRINCIPAL

ENERGY LEVEL (n)

(n – 1) POSSIBLE (l)

VALUES: 0 TO (n – 1)

SUBLEVELS

1 1 – 1 = 0 0 s2 2 – 1 = 1 0,1 s,p3 3 – 1 = 2 0,1,2 s,p,d4 4 – 1 = 3 0,1,2,3 s,p,d,f5 5 – 1 = 4 0,1,2,3,4 s,p,d,f,g6 6 – 1 = 5 0,1,2,3,4,5 s,p,d,f,g,h

MAGNETIC QUANTUM NUMBER (ml)

• Describes the orientation

of the atomic orbital in space. The magnetic quantum number can only have (2l X 1) integral values for a particular l.

• Example:

l = 1[ (2 X 1) + 3] or 3 ml

Values. These 3 ml values are -1, 0, and +1

+N

N

+

n=1n=2n=3

n= so on…

K L M

NUMBER OF ATOMIC ORBITALS PER SUBLEVEL

n l SUBLEVEL 2l + 1 ml VALUES Number of Atomic Orbital

1 0 1s 2(0) + = 1 0 12 0 2s 2(0) + = 1 0 13 1 2p 2(1) + = 3 1, 0, -1 3

0 3s 2(0) + = 1 0 11 3p 2(1) + = 3 1, 0, -1 32 3d 2(2) + = 5 2, 1, 0, -1, -2 5

ELECTRON SPIN QUANTUM NUMBER (ms)

• Describes the spin direction of an electron. There are only two possible values for the electron spin quantum number, and these are + ½ and – ½.

• ms = + ½ (clockwise)

• ms = - ½ (counter-clockwise)

+N

N

+

n=1n=2n=3

n= so on…

K L M

ELECTRON CONFIGURATION

PAULI’S EXCLUSION PRINCIPLE• Wolfgang Pauli• States that no two electron can be described by the

same four quantum numbers. • Two electrons may have the same first three quantum

numbers (n, l, ml) but these two electrons must

have different spins (ms).

• Pauli’s exclusion principle implies that each orbital in an atom can hold at most two electrons and that two electrons must have opposite spin.

THE AUFBAU PRINCIPLE• Principle applies the laws in QUANTUM MECHANICS to

the distribution of electrons among energy levels in the ground states (most stable states) of atoms.

• The word AUFBAU means “building up” in german.

• The principle describes a hypothetical process in which the electrons are imagined as entering the atomic orbitals one by one. The process results in obtaining the electron configuration of an atom in its ground state.

Electron Filling Order

5s

4s

3s

2s

1s

2p

3p

4p

3d

4dE

N

E

R

G

Y

Writing Atomic Electron Configurations

11 s

value of nvalue of l

# of e

spdf notationfor H, atomic # = 1

2 ways of writing

configs. One is

called the spdf

notation.

Other is called the orbital box notation.

Arrowsdepictelectronspin

ORBITAL BOX NOTATIONfor He, atomic number = 2

1s

21 s

Relation between orbital filling & the periodic table

Electron Arrangement in Atoms

Electron Arrangement in Atoms

Electrons in atoms are arranged as:

SHELLS (n)

SUBSHELLS (l)

ORBITALS (ml)