Many electron atoms and the Periodic Table

1

Many electron

atoms and the

Periodic Table

2

Objectives

 Explain the scientific basis for the Periodic Table

 Apply the Aufbau principle, the Pauli Exclusion principle and Hund’s rule to electrons in an atom

 Explain the concept of energy levels in an atom and the order of filling these levels

 Write the electronic configuration of the first 20 elements

 Draw and explain a block diagram of the Periodic Table

 Explain the meaning and position of the transition elements

 Explain the periodic variations of atomic size, ionisation energy, electron affinity and electronegativity

3

The Periodic Law



The physical and chemical properties of the elements are a function of the electronic

configuration of the their atoms which vary with increasing atomic number in a periodic manner



hence the Periodic Table

 elements are grouped according to their electronic structure

 provides information on chemical properties

4

Many Electron Atoms



Describe in terms of hydrogen orbitals

 Same quantum numbers and shapes

 energies different



For Hydrogen:

 Depend on n

3s, 3p, 3d all the same energy



For many e

atom:

 Different subshells at different energies 2s < 2p depend on n and l

5

Orbital Energies

Energy

1s 1s

n=1 n=3

n=2

2s 2p

3s 3p 3d

0

n=1 n=3

n=2

2s

2p 3s

3p

3d 0

Energy

n=4

4s

Hydrogen Many e^- Atoms

Need to consider Effect of increased nuclear charge Repulsions between electrons

6

Effective Nuclear Charge

Z

e^- of interest

3 e^- found in sphere

Eff. Nuclear charge = 5 - 3 = 2

Assume 5

 Net positive charge from nucleus attracting an electron

 electron shielded by inner e^-

 effective nuclear charge Z_eff = Z - S

S = No. of e^- between atom and nucleus

 hence outer shell e^- experience less + charge

 effect of “screening” depends on e^- distribution

 need to consider orbital shape

7

Orbital shape and Energy



s-orbital e

can be close to nucleus



p-orbital further away than an “s” e



d-orbital further from nucleus than “p” e



therefore,

 “s” e^- has least screening by other e^-

 so a larger effective nuclear charge and is more tightly bound

(lower energy than “p” ie. more stable)

8

Order of Energy Levels for many e

Atom

In general, 1s < 2s < 2p < 3s < 3p…...

9

An easy way to remember…...

1s

3d

5p 4p 3p 2p

5s 4s 3s

6d

5f 4f 5d

4d 2s

6s 6p

Increasing Energy

10

Energy

11



need to consider another property of electrons to determine how electrons populate orbitals



envisage electron as spinning on own axis

 quantized

 only 2 spin states

 distinguished by the spin -magnetic quantum number m_s

Electron Spin

+ 1 2

1 - 2

12

Electron Spin



Stern-Gerlach experiment - when a beam of ground state H atoms (1s) is passed through a magnetic field, the beam splits into two beams

REMIND!

13

Pauli and Hund

Pauli Exclusion Principle



no two electrons in an atom can have the same 4 quantum numbers



there are only 2 values of m



hence, an orbital can only hold 2 electrons and they must have opposite spins

Hund’s Rule



If orbitals have the same energy, add electrons

singly with spins parallel first

14

The Aufbau Principle

Building up



fill available orbitals with available electrons

starting with lowest energy orbitals (most stable)



this gives ground state Note



don’t forget Pauli and Hund!!

Building up atoms

Aufbau Principle



The aufbau

principle shows how orbitals are filled: in the

order to the left.

Two extra rules are needed.

shell 1 shell 2 shell 3 shell 4 3d

1s

2s 2p

3s

3p 4s

4p 4d

Increasing

energy

17

Aufbau Principle-2

 Hund’s rule states that when filling a set of orbitals at the same energy (sunshell), one electron is placed in each orbital before pairing occurs.

 Pauli’s principle tells us that when placing a second electron in an orbital, its spin must be opposite to the electron already in the orbital. (Spin is usually

represented by an arrow in an orbital box.)

Aufbau Principle-3a



“Box” or “orbital diagrams for electron configurations.

H (1e)

1S He (2e)

1S

The 1s orbital is filled.

Second electron is paired. (Pauli)

Start at 1s

Aufbau Principle-3b

Li (3e)

1S 2S ^1s

^{, 2s}

C (6e)

1S 2S 2p

Hund’s rule applies to p subshell

1s

, 2s

, 2p

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Aufbau Principle-3c

 In 2p subshell, Hund’s rule! Next electron follows Pauli principle

O (8e)

1S 2S 2p _1s

_{, 2s}

_{, 2p}

Ti (22e)

(22e)

4S 3d

1s ² , 2s ² , 2p ⁶ , 3s ² ,

3p ⁶ , 4s ² , 3d ²

21

Electrons and the Periodic Table

 Electron fit logically into the periodic table. The s block

elements (see next slide) start filling at level 1, the p block at level 2, and the d block at level 3.

22

Excited State Atoms



Occur when energy has been supplied to raise e

energy

Ne

1s

2s

2p

Ground state

1s

2s

2p

….5s

High energy excited state

1s

2s

2p

….3p

Low energy excited state

23

Transition metals

Consider the elements in the 4th period (after Ar 1s

2s

2p

3s

3p

)



after 3p natural sequence would be 3d



but 4s has (slightly) lower energy than3d



according to Aufbau must fill 4s before 3d

 ground state for K is [Ar]4s¹ and Ca is [Ar]4s²



as charge increases the energy of 3d decreases

 in Sc 3d < 4s

 Sc⁺ [Ar]3d¹4s¹ Sc²⁺[Ar]3d¹

24

Transition metals



energy drop in 3d continues through to Zn



consequences

 for elements Cu  Zn oxidation state 1+ or 2+

 beyond Zn 3d electrons have no chemical role



elements from Sc to Zn called d-block elements

 filling up the d orbital

25

Transition metals



anomalies

 Cr [Ar]3d⁵4s¹ expect [Ar]3d⁴4s²

 Cu [Ar]3d¹⁰4s¹ expect [Ar]3d⁹4s²

 similar occur in fifth period

 also Ru [Kr]4d⁷5s¹ expect [Kr]4d⁶5s²



sixth period filling is erratic

 energies of 4f, 5d & 6s comparable



seventh period all are radioactive

26

The Periodic Table

Organisation of the elements

 electronic configurations related to position of element

 elements grouped according to type of orbital the outer shell electrons are in

BLOCK: Named for last subshell occupied GROUP: the columns

 all elements have same outer orbital e^- configuration

 similar chemical properties

PERIODS: rows

 all elements same shell

27

The Periodic Table



Subshell

orbitals with same energy eg. 2p



Shell

orbitals with similar energy eg. 2s, 2p



Valence Electrons

occupy outermost shell



Core Electrons

occupy filled inner shells Cl 1s²2s²2p⁶ 3s²3p⁵ Ne core valence



Closed Shell Atoms

full outer shell - very stable - noble gases

28

29

Periodic Properties

Predicted by considering e

configurations



Sizes of atoms and ions



Ionisation energies



Electron affinities



Electronegativities



Polarising powers and polarisabilities

30

Sizes Of Atoms and Ions

Atoms do not have sharply defined boundaries



Hence, need to define atomic size



Atomic size depends on chemical environment

 ie. Bonding etc

31

32

This shielding means that each valence electron in effect only

“feels” a +1 charge form the nucleus; this occurs for an highly excited valence electron. Otherwise the shielding makes the “seen”

charge is higher than +1

33

Defining Atomic and Ionic Size

2r

estimating size

atomic radius = half the

distance between nearest atoms in element (in condensed phases)

for ions, base ionic radii on interatomic

distance in ionic crystals. (depends on charge...)

Cu Cu Cu⁺ Cu⁺²

atom covalent bonding

1.28 1.17 0.96 0.69 A^o

34

Sizes of Atoms and Ions

Decrease Increase

Why?

Consider:

1. Principle Quantum number (shell)

2. Effective nuclear charge

35

Increase nuclear charge

but no. of core electrons stay the same

so effective nuclear charge increases while shell remains the same

hence electrons drawn closer to nucleus hence decrease atomic size

eg. Na 1s

2s

2p

3s

1.91A

Mg 1s

2s

2p

3s

1.60 A

Across a Period…….

36

Down A Group….



More distant electron shell occupied while effective nuclear charge the same



hence atomic size increases

eg. Li 1s

2s

1.57 A

Na 1s

2s

2p

3s

1.91 A

Atomic

radii

38

Radius of Ions

Cation < Atom

eg. Na

< Na

0.96 Ao 1.91 A^o

1s

2s

2p

1s

2s

2p

3s



lost an e

core electrons exposed more tightly bound

Decreases across a period eg. Na

> Mg

39

Radius of Ions

Atom < Anion

eg. Cl < Cl

0.99 Ao 1.81 A^o

[Ne]3s

3p

[Ne]3s

3p



gained an e

electron cloud greater

decreases nuclear pull by each electron

Decreases across a period e.g. S

> Cl

40

Ionisation Energy

The energy required to remove an electron from a ground state atom

X

 X

+ e

E = IE

Measure of stability of outer shell electron configuration

 Depends on

 size of the atom

 effective nuclear charge

 screening effect of inner electrons

 type of electron

41

Ionisation Energy

Increase

Decrease Why?

Consider

1. Effective nuclear charge 2. Distance of e^- from nucleus

42

Across a Period….

Increase in effective nuclear charge Decrease in radius

hence increase attraction between e^- and nucleus hence increase IE

Exceptions: “p” less stable than “s” (B < Be)

orbitals “singly occupied” more stable than “doubly occupied” (O < N)

43

Down a Group…...

Increase radius while

effective nuclear charge the same

hence Decrease attraction between e^- and nucleus hence decrease IE

Ionization energy

45

Electron Affinity

The energy released when an e

added to atom to form anion

eg. F_(g) + e^-  F_-(g) EA = 328 kJ/mol

 a small EA means e^- must be forced to stick

 measure of ability of atom to accept e^-

46

Electron Affinities

Same as IE Why?

Consider 1. Size

2. Effective Nuclear charge Increase

Decrease

Low for Noble gases

47

Electron Affinities

1. F + e^-  F^- EA = 328.0 kJ mol^-1 1s² 2s² 2p⁶

- stable closed shell = Ne

2. Ne + e^-  Ne^- EA = negative 1s² 2s² 2p⁶ 3s¹

- new shell, further from nucleus

- almost totally screened from nuclear charge - so unstable

48

Electron Affinities

Be 1s²2s² Low EA Filled s subshell

Next e^- higher energy level so need energy to add e^-

N 1s²2s²2p³ Low EA Half filled “p”

Adding another e^- will cause e^- repulsion hence unfavourable

49

Electronegativity

The ability of an atom to draw e

to itself in a chemical bond

useful for

predicting extent of charge transfer between atoms

eg. “Covalent”  “Ionic”

H—H C—H N—H NaCl

50

Electronegativity

Related to EA and IE

Cs and F IE₁ EA

Cs low small

F high large

(Cs gives up e^- easily, while F accepts e^- easily.) Electron acceptor Electronegative Electron donor

Electropositive

51

Electronegativity

Increase Decrease

( size, nuclear charge )

Size, same effective nuclear charge

52

Electronegativity and Bond Type

Numerical scale of electronegativities developed Paulings electronegativity scale 







For two bonded atoms

(), is a measure of the bond polarity

with the more electronegative atom having more

of the electron density

53

Electronegativity and Bond Type

H^+Cl^- Examples

Na Cl

(0.93) (3.16) () = 2.23, ionic, Na⁺Cl^-

H Cl

(2.20) (3.16) () = 0.96, polar covalent

Cl Cl

(3.16) (3.16) () = 0, covalent, Cl-Cl

>2.0

<0.4