lecture 21 & 22...orbital shape magnetic m l integers from -l to 0 to +l orbital orientation...

ANNOUNCEMENTS• Chapter 5 homework due Friday March 6.

• Chapter 6 homework due Friday March 13.

• Quiz 2 due Thursday March 12 and Exam 2 is March 14.

• Review the exam (learn from your mistakes)

• Go to the help room GMCS-212

• Go to the Supplemental Instruction sessions

QUANTUM NUMBERS1

0

0

2 3

0 1 0 1 2

-1,0,1

2p1s

0

2s

-1,0,1

3p

0

3s

-2,-1,0,1,2

3d

Principal: n(size, energy)

Angular momentum: l

(shape)

Magnetic: ml

(orientation)

Orbital:

NAMING ATOMIC ORBITALS• An atomic orbital is designated by its value for n (level)

and l (sublevel).

• In naming, the level (n value) is used directly, the sublevel (l value) is expressed as a letter :

• l = 0 - s (sharp)

• l = 1 - p (principal)

• l = 2 - d (diffuse)

• l = 3 - f (fundamental)

PROBLEMThe set of quantum numbers below is not allowed.

Assuming that both the n and ml values are correct, what value should l be in order for the quantum number to be

allowable?n = 3, l = 0, ml = -2

(a) l = 1 (b) l = 2(c) l = 4(d) l = -1(e) l = -2

1s 2s 3s

1s: n = 1 , l = 0, ml = 0

2P ATOMIC ORBITAL

n = 2 , l = 1, ml = -1, 0, 1

3D ATOMIC ORBITALn = 3 , l = 2, ml = -2, -1, 0, 1, 2

4F ORBITAL

This is one of the seven different f orbitals.

The larger orbitals are more complex with more lobes and

nodes in their structure.

ORBITAL NAMING

• n = 2 , l = 0

• n = 3 , l = 1

• n = 4 , ml = +3

• n = 2 , l = 1

What are the names of these orbitals?

HYDROGEN ATOM BEAM• Hydrogen atoms have one proton and one electron.

• Every hydrogen atom should be the same.

• Pass a beam of H atoms through a magnetic field and the atoms separate into two paths.

SUMMARY OF QUANTUM NUMBERS OF ELECTRONS IN ATOMS

Name Symbol Permitted Values Property

principal n Positive integers (1,2,3...)

Orbital energy (size)

angular momentum l Integers from 0

to n-1 Orbital shape

magnetic mlIntegers from -l

to 0 to +lOrbital

orientation

spin ms +½ or -½ Direction of e- spin

Spin up = +½ ↑Spin down = -½ ↓

Two e- per orbital: ↑↓spin paired

QUANTUM NUMBERS & ELECTRONS

1

0

0

2 3

0 1 0 1 2

-1,0,10 -1,0,10 -2,-1,0,1,2

Principal: n(size, energy)

Angular momentum: l

(shape)

Magnetic: ml

(orientation)

Electrons: 2e- 2e- 2e-6e- 6e- 10e-

PAULI EXCLUSION PRINCIPLE• Two electrons that are in the same atom cannot have the

same set of quantum numbers.

• Each electron in an atom must have its own unique set of quantum numbers (its own unique identity)

• Allowed configuration - abides by the Exclusion Principle

• Forbidden configuration - violates the Exclusion Principle

WHAT IS THE GROUND STATE CONFIGURATION FOR HELIUM?Ground state electron configuration for hydrogen:

H = 1s1 (one electron with a 1s orbital wavefunction)

Ground state electron configuration for helium:

He = 1s2 (two electrons with 1s orbital wavefunctions)

Quantum numbers for each He e-:n = 1, l = 0, ml = 0, ms = +½n = 1, l = 0, ml = 0, ms = -½

ELECTRONS ON ATOMSHydrogen Electron Helium Electrons

Ener

gy (J

)

0

1s

2s

Ener

gy (J

)

0

1s

2s

ORDER OF FILLING SUBLEVELSElectrons occupy orbitals based on the Aufbau principle, they fill the

lowest subshells first and build up from there.

MANY-ELECTON ATOM ENERGY DIAGRAM

QUESTIONHow many electrons in an atom can be

in a 4p orbital?

Answer:A: 2B: 3C: 4D: 6E: 8

4p 4p 4p

QUESTIONIn an atom, what is the maximum number of

electrons that can have the quantum numbers: n = 4 and ms = +½

Answer:A: 4B: 8C: 16D: 32E: 64

LECTURE OBJECTIVES• Chapter 6.3

• Use quantum numbers to express specific electronic orbitals.

• Apply appropriate rules to the filling of electrons in atomic orbitals.

• Chapter 6.4

• Derive the predicted ground-state electron configurations of atoms

• Identify and explain exceptions to predicted electron configurations for atoms and ions

• Relate electron configurations to element classifications in the periodic table

• Chapter 6.5

• Describe and explain the observed trends in atomic size, ionization energy, and electron affinity of the elements

QUESTIONWhat is the ground state electronic

configuration of lithium (Z = 3)?

2p3

2s22p1

1s22p1

1s22s1

1s3

Answer:ABCDE

GROUND STATE CONFIGURATION OF LITHIUM

• Lithium (three electrons):

• Pauli exclusion principle prevents all three electrons from being in the 1s level (Li ≠ 1s3)

• So where does the third electron go; 2s or 2p level?

• The 2s orbital is able to penetrate closer to the nucleus, making it more stable and favored by the electron.

THE EFFECT OF L ON ENERGY

ENERGY STATES OF ATOMS• Ground State

• Lowest energy arrangement of electrons in an atom: Li = 1s22s1

• Excited State

• Any allowed electron configuration that is not the ground state: Li = 1s22p1

• Forbidden State

• Impossible electron configurations (Pauli): Li = 1s3

Hund’s Rule:Lowest energy state occurs when there are the greatest number of

unpaired electrons with parallel spins.

ORBITAL FILLING

Pairing of electrons only occurs when all sublevels of the orbital have an electron.

WRITING ELECTRON CONFIGURATIONS

1s22s1

1s22s2

1s22s22p1

1s22s22p2

1s22s22p3

1s22s22p4

1s22s22p5

1s22s22p6

Li =Be =B =C =N =O =F =

Ne =

FullLi =

Be =B =C =N =O =F =

Ne =

[He]2s1

[He]2s2

[He]2s22p1

[He]2s22p2

[He]2s22p3

[He]2s22p4

[He]2s22p5

[He]2s22p6

Condensed

CLASSIFYING ELECTRONS IN AN ATOM

• Valence Electrons

• Electrons in the highest energy level of the atom are valence electrons - electrons with the largest value for n.

• Valence electrons are the ones that are chemically important.

• Core Electrons

• Electrons in the filled lower energy levels of the atom.

ELECTRON CONFIGURATIONS FOR GROUPS

Group 2Be =Mg =Ca =Sr =Ba =

[He]2s2

[Ne]3s2

[Ar]4s2

[Kr]5s2

[Xe]6s2

2 valance electrons

[He]2s22p5

[Ne]3s23p5

[Ar]3d104s24p5

[Kr]4d105s25p5

F =Cl =Br =

I =

Group 7

7 valance electrons

TRANSITION METALS

• The transition metals have electrons in the d orbitals.

• There are a pair of exceptions to the normal electron filling in the transition metals (Cr and Cu).

• These exceptions occur because they are lower in energy than the normal electron filling pattern.

• The exception continues down those groups (Cr, Mo, W & Cu, Ag, Au).

WHAT AFFECTS ATOMIC ORBITAL ENERGIES?

• The Nuclear Charge (Zeffective)

• Higher nuclear charge lowers orbital energy (stabilizes the system) by increasing the nucleus-electron attractions.

• Electron Repulsions (Shielding)

• Additional electrons in the same orbital raise orbital energy through electron-electron repulsions.

• Additional electrons in inner orbitals shield outer electrons more effectively than do electrons in the same sublevel.

EFFECTIVE NUCLEAR CHARGE (ZEFF)

• The nuclear charge “experienced” by an electron in a many-electron atom is not the same as the actual charge of the nucleus.

• Zeff is specific for each electron in the atom.

• Zeff is always less than the full nuclear charge (Z) of the atom, due to electron shielding.

• For a 1s electron in a helium atom (Z=2), Zeff = +1.69

QUESTIONFor which of these one-electron species is it

most difficult to remove the electron?

He+

Li2+

Be3+

B4+

Don’t know

Answer:ABCDE

ATOMIC PROPERTIES• Group Trends

• Variations in atoms of the same group are principally due to differences in the principal quantum number (n) for the valence electrons. (e.g. O, S, Se, Te, Po)

• Periodic Trends

• Variations in atoms along a period are principally due to the differences in the Zeff of the nucleus (e.g. B, C, N, O, F)

ATOMIC RADII• Atoms are, as you would expect, very small. The size of atoms is

typically measured in picometers (pm): 1 pm = 1×10-12 m or in Ångstroms (Å): 1Å = 1×10-10 m; 1Å = 100 pm

• The atomic radius is the sphere around the nucleus limited to the distances which the electrons can reach.

• The radius of an atom is not a fixed quantity; it will vary depending on the environment of the atom.

• The atomic radius is determined through measurements of the internuclear distances of molecules and compounds.

METALLIC RADII

• Defined as half the shortest distance between nuclei of adjacent atoms in a crystal of the element.

• Aluminum:

• Internuclear distance: 286 pm

• Atomic radius: 143 pm

COVALENT RADII• Two ways of determining the

covalent radius of an atom:

• Measured as half the bond length for the diatomic molecule (e.g. O2).

• By measuring the bond length between two atoms (e.g. CO) when the covalent radius of one of the atoms is known (e.g. O).

MAIN-GROUP ATOMIC RADII

The atomic radii of the main-group elements increase down each group and from left to right across a period.

Transition elements are less systematic.

PERIODICITY OF ATOMIC RADII

QUESTIONWhich sequence of atoms is listed in

the correctly in order of increasing size?

F < Br < Ge < KNa < Al < P < S

Ba < Ca <Mg < BeCl < Si < C < B

Answer:ABCD

IONIZATION ENERGY (IE)• The ionization energy is the energy needed to remove

an electron from a gas phase atom or ion.

• A(g) → A+(g) + e-(g) ∆E = IE1 for A

• A+(g) → A2+(g) + e-(g) ∆E = IE2

• The ionization energies are always positive and always increase for each subsequent electron to be removed.

• IE1 < IE2 < IE3 < ...

IONIZATION ENERGIES

• Beryllium (1s22s2) ionization energies increase as follows:

• IE1 = + 900 kJ/mol (1s22s1)

• IE2 = + 1,760 kJ/mol (1s2)

• IE3 = + 14,850 kJ/mol (1s1)

• Removal of core electrons requires much more energy.

IONIZATION ENERGY TREND

IONIZATION ENERGY (IE)Which element has the greatest first

ionization energy (IE1)?

Li - [He]2s1

Na - [Ne]3s1

C - [He]2s22p2

O - [He]2s22p4

520 kJ/mol

496 kJ/mol

1086 kJ/mol

1314 kJ/mol

152 pm

186 pm

77 pm

73 pm

PERIODICITY OF IONIZATION ENERGIES (IE1)

First ionization energies of the main-group elements.

Generally increase up the groups and increase from left to right across a period.

QUESTIONList these atoms in order of increasing first

ionization energy: Li, Na, C, O, F

Li < Na < C < O < FNa < Li < C < O < FF < O < C < Li < NaNa < Li < C < F < O

Answer:ABCD

ELECTRON AFFINITY (EA)

• The electron affinity is the energy change (∆E) associated with adding an electron to a gas phase atom or ion.

• A(g) + e-(g) → A-(g) ∆E = EA1 for A

• The electron affinities can be either positive or negative - depending on the specific element.

• Periodic trends for EA are not as obvious as IE or radius.

Main-group electron affinities.

IONIC RADII

• The ionic radius is a measure of the size of ions.

• The radius can vary dramatically based on the environment that the ion is found within.

• The ionic radius is determined through measurements of the internuclear distances of ionic compounds.

IONIC RADII TRENDS• Cations are smaller than their parent atoms:

• Li = 152 pm Li+ = 76 pm

• Anions are larger than their parent atoms:

• F = 72 pm F- = 133 pm

• The ionic radii increase down a group

• Li+ = 76 pm Na+ = 102 pm

PROBLEMWhich ion has the largest radius?

Ion Electrons Protons Radius

Ca2+ 18 20 100 pm

Cl- 18 17 181 pm

K+ 18 19 138 pm

S2- 18 16 184 pm

IONIC RADII

Have valence electrons equivalent to Neon (ioselectronic ions)

MAIN-GROUP IONS & NOBLE GAS CONFIGURATIONS