Electronic Structure III. Quantum Numbers, Electronic ......•The principal quantum number, n, is a positive integer that indicates the shell and relative sizes and energies of orbital(s)

Electronic Structure III. Quantum Numbers, Electronic Structure, and

Electron Configuration

Quantum numbers tell us where an atom's electrons can be found.

• Electrons share the space around nuclei.

• Quantum numbers tell us where the electrons are and how much energy they have.

• Each electron in an atom has a unique set of four quantum numbers. No two electrons can have the same four quantum numbers.

• All that can be known about an electron – its position, energy, etc. – isspecified completely within its complete set of quantum numbers.

• The quantum numbers of electrons and the mathematical expressions in which they are used form the basis of quantum mechanics.

Quantum Mechanics

• The description of the behavior of particles as waves is a branch of physics called quantum mechanics.

• Quantum mechanics uses wave equations to describe the behavior of electrons and other sub-atomic particles.

• Here's one such wave equation, called the Schrödinger Equation, that's used to provide information about electrons:

• At this level, we will skip the equations and study only what the quantum numbers n, l, ml, and ms mean.

!

− ℏ$2&'

(

)

1+$

∂∂+ +$ -∂./012(+, 5, 6

∂+ + 1+$sin 5

∂∂5 sin 5 -∂./012(+, 5, 6

∂5

+ 1+$sin2 5

-∂$./012(+, 5, 6∂6$ + ;$

4=>?+./012(+, 5, 6) = B/012./012(+, 5, 6

An electrons's four quantum numbers tell us everything.

• The principal quantum number, n, is a positive integer that indicates the shell and relative sizes and energies of orbital(s).

• The angular momentum quantum number, l, is an integer from zero to n-1. It defines the shape of the orbitals.Value of l 0 1 2 3 4 Letter identifier s p d f g

• The magnetic quantum number, ml, is an integer with a value from -lto +l. It defines the orientation of an orbital in the space around the nucleus of an atom and the number of orbitals in a subshell.

• The spin magnetic quantum number, ms, is to account for the two possible orientations of electron "spin." The two values for ms are +1/2 and -1/2.

Here's are the possible values for n, l, ml, and ms.

Practice: Which of the following combinations of quantum number are allowed?1. n = 1, l = 1, ml = 02. n = 3, l = 0, ml = 03. n = 1, l = 0, ml = -14. n = 2, l = 1, ml = 2

These are the only allowed combinations of quantum

numbers.

This table stops at n = 4.

Each type of orbital has a different shape, or set of shapes.

These orbitals were determined exactly for hydrogen, however, we can use them to approximate the orbitals for other atoms.

ssubshell

psubshell

d

subshell

l = 0: s orbital

l = 0: p orbital

l = 2: d orbital

The three p orbitals plotted together in 3-D space shows how they share the same space around the nucleus.

p orbitals

l =1

not ml=(1,0,-1) – just say there's "three" p orbitals

Electrons are represented by "orbitals."

The orbitals are not like the rings in the Bohr model, they fill up space.

n=1, l=0

“s” orbital

principal quantum number

angular momentum quantum number l=0:

s orbitals are shaped like spheres.

n=2, l=0

“s” orbital



The size of an s orbital increases with n.

n=3, l=0

“s” orbital



The orbital is what the wave function looks like in space.

The square of the wave function gives the electron density.

n=4, l=0

“s” orbital



Electrons p orbitals occupy opposite sides of the nucleus.

n=2, l=1

“p” orbital



When an electron loses energy, its quantum numbers change.

n=4, l=1

n=2, l=0

n=4, l=1486.1 nm

When an electron loses energy, its quantum numbers change.

There are rules for assigning electrons to orbitals.

• Pauli Exclusion PrincipleNo two electrons can have the exact same 4 quantum numbers.

n=4, l=0, ml=0, ms= +1/2 n=4, l=0, ml=0, ms= -1/2

• Aufbau PrincipleElectrons fill the lowerst-energy orbitals first.

• Hund's RuleIf electrons are filling orbitals in the same subshell, they don't pair up, but rather they spread out.

Each type of orbital can "hold" two electrons.

Pauli Exclusion PrincipleNo two electrons can have the exact same 4 quantum numbers

First electron:n=4, l=0, ml=0, ms= +1/2

Second electron:n=4, l=0, ml=0, ms= -1/2

If n, l, and ml are the same for two electrons, then they are in the same orbital and their spins must be different.

Practice assigning electrons to orbitals in accordance with the aufbau principle.

Draw boxes for the orbitals instead of atoms

Practice - Answers

Remember, these quantum numbers and orbitals were determined exactly for hydrogen, however, we can use them to approximate the orbitals for other atoms.

The electron configuration is a code for the quantum numbers of all the electrons in an atom, ion, or molecule.

Electron Configuration

Here are more examples of electron configurations.

• Filling of orbitals in C, N, O, F, and Ne follows Hund's rule

• For a 1-electron atoms such as hydrogen, all orbitals of a given value of n have the same energy, like this:

Energies of higher orbitals get a bit out of order.

• For multielectron atoms, all orbitals of a given value of n do not have the same energy.

• The energy spacing decreases as nincreases. This happens differently for s, p, d, and f orbitals.

• The energies of different values of nbegin to overtake one another. For example, 4s is lower in energy than 3d

Because 3d has a lower energy than 4s, the electron configuration must allow this.

Electron configurations follow the organization of the periodic table.

The Periodic Table of the Elements1H

Hydrogen1.00794

2HeHelium4.003

3Li

Lithium6.941

4Be

Beryllium9.012182

5B

Boron10.811

6C

Carbon12.0107

7N

Nitrogen14.00674

8O

Oxygen15.9994

9F

Fluorine18.9984032

10NeNeon

20.1797

11NaSodium

22.989770

12Mg

Magnesium24.3050

13Al

Aluminum26.981538

14Si

Silicon28.0855

15P

Phosphorus30.973761

16S

Sulfur32.066

17Cl

Chlorine35.4527

18ArArgon

39.94819K

Potassium39.0983

20Ca

Calcium40.078

21Sc

Scandium44.955910

22Ti

Titanium47.867

23V

Vanadium50.9415

24Cr

Chromium51.9961

25Mn

Manganese54.938049

26FeIron

55.845

27CoCobalt

58.933200

28NiNickel

58.6934

29CuCopper

63.546

30Zn

Zinc65.39

31GaGallium69.723

32Ge

Germanium72.61

33AsArsenic

74.92160

34Se

Selenium78.96

35Br

Bromine79.904

36Kr

Krypton83.80

37Rb

Rubidium85.4678

38Sr

Strontium87.62

39Y

Yttrium88.90585

40Zr

Zirconium91.224

41Nb

Niobium92.90638

42Mo

Molybdenum95.94

43Tc

Technetium(98)

44Ru

Ruthenium101.07

45Rh

Rhodium102.90550

46Pd

Palladium106.42

47AgSilver

107.8682

48Cd

Cadmium112.411

49In

Indium114.818

50Sn

Tin118.710

51Sb

Antimony121.760

52Te

Tellurium127.60

53I

Iodine126.90447

54XeXenon

131.29

55CsCesium

132.90545

56BaBarium

137.327

57La

Lanthanum138.9055

72Hf

Hafnium178.49

73Ta

Tantalum180.9479

74W

Tungsten183.84

75Re

Rhenium186.207

76Os

Osmium190.23

77Ir

Iridium192.217

78Pt

Platinum195.078

79AuGold

196.96655

80HgMercury200.59

81Tl

Thallium204.3833

82PbLead

207.2

83Bi

Bismuth208.98038

84Po

Polonium(209)

85At

Astatine(210)

86RnRadon(222)

87Fr

Francium(223)

88RaRadium(226)

89Ac

Actinium(227)

104Rf

Rutherfordium(261)

105Db

Dubnium(262)

106Sg

Seaborgium(263)

107Bh

Bohrium(262)

108Hs

Hassium(265)

109Mt

Meitnerium(266)

110

(269)

111

(272)

112

(277)

113 114

58CeCerium

140.116

59Pr

Praseodymium140.90765

60Nd

Neodymium144.24

61Pm

Promethium(145)

62Sm

Samarium150.36

63Eu

Europium151.964

64Gd

Gadolinium157.25

65Tb

Terbium158.92534

66Dy

Dysprosium162.50

67Ho

Holmium164.93032

68ErErbium

167.26

69TmThulium

168.93421

70Yb

Ytterbium173.04

71Lu

Lutetium174.967

90Th

Thorium232.0381

91Pa

Protactinium231.03588

92U

Uranium238.0289

93Np

Neptunium(237)

94Pu

Plutonium(244)

95Am

Americium(243)

96CmCurium(247)

97Bk

Berkelium(247)

98Cf

Californium(251)

99Es

Einsteinium(252)

100FmFermium(257)

101Md

Mendelevium(258)

102No

Nobelium(259)

103Lr

Lawrencium(262)

1995 IUPAC masses and Approved Names from http://www.chem.qmw.ac.uk/iupac/AtWt/masses for 107-111 from C&EN, March 13, 1995, p. 35112 from http://www.gsi.de/z112e.html

n = 1

n = 2

n = 3

n = 4

He

n = 5

n = 6

n = 7

(n-1)d fills first, then np

ns fillsnp fills

f orbitals fill




The Periodic Table of the Elements1H

Hydrogen1.00794

2HeHelium4.003

3Li

Lithium6.941

4Be

Beryllium9.012182

5B

Boron10.811

6C

Carbon12.0107

7N

Nitrogen14.00674

8O

Oxygen15.9994

9F

Fluorine18.9984032

10NeNeon

20.1797

11NaSodium

22.989770

12Mg

Magnesium24.3050

13Al

Aluminum26.981538

14Si

Silicon28.0855

15P

Phosphorus30.973761

16S

Sulfur32.066

17Cl

Chlorine35.4527

18ArArgon

39.94819K

Potassium39.0983

20Ca

Calcium40.078

21Sc

Scandium44.955910

22Ti

Titanium47.867

23V

Vanadium50.9415

24Cr

Chromium51.9961

25Mn

Manganese54.938049

26FeIron

55.845

27CoCobalt

58.933200

28NiNickel

58.6934

29CuCopper

63.546

30Zn

Zinc65.39

31GaGallium69.723

32Ge

Germanium72.61

33AsArsenic

74.92160

34Se

Selenium78.96

35Br

Bromine79.904

36Kr

Krypton83.80

37Rb

Rubidium85.4678

38Sr

Strontium87.62

39Y

Yttrium88.90585

40Zr

Zirconium91.224

41Nb

Niobium92.90638

42Mo

Molybdenum95.94

43Tc

Technetium(98)

44Ru

Ruthenium101.07

45Rh

Rhodium102.90550

46Pd

Palladium106.42

47AgSilver

107.8682

48Cd

Cadmium112.411

49In

Indium114.818

50Sn

Tin118.710

51Sb

Antimony121.760

52Te

Tellurium127.60

53I

Iodine126.90447

54XeXenon

131.29

55CsCesium

132.90545

56BaBarium

137.327

57La

Lanthanum138.9055

72Hf

Hafnium178.49

73Ta

Tantalum180.9479

74W

Tungsten183.84

75Re

Rhenium186.207

76Os

Osmium190.23

77Ir

Iridium192.217

78Pt

Platinum195.078

79AuGold

196.96655

80HgMercury200.59

81Tl

Thallium204.3833

82PbLead

207.2

83Bi

Bismuth208.98038

84Po

Polonium(209)

85At

Astatine(210)

86RnRadon(222)

87Fr

Francium(223)

88RaRadium(226)

89Ac

Actinium(227)

104Rf

Rutherfordium(261)

105Db

Dubnium(262)

106Sg

Seaborgium(263)

107Bh

Bohrium(262)

108Hs

Hassium(265)

109Mt

Meitnerium(266)

110

(269)

111

(272)

112

(277)

113 114

58CeCerium

140.116

59Pr

Praseodymium140.90765

60Nd

Neodymium144.24

61Pm

Promethium(145)

62Sm

Samarium150.36

63Eu

Europium151.964

64Gd

Gadolinium157.25

65Tb

Terbium158.92534

66Dy

Dysprosium162.50

67Ho

Holmium164.93032

68ErErbium

167.26

69TmThulium

168.93421

70Yb

Ytterbium173.04

71Lu

Lutetium174.967

90Th

Thorium232.0381

91Pa

Protactinium231.03588

92U

Uranium238.0289

93Np

Neptunium(237)

94Pu

Plutonium(244)

95Am

Americium(243)

96CmCurium(247)

97Bk

Berkelium(247)

98Cf

Californium(251)

99Es

Einsteinium(252)

100FmFermium(257)

101Md

Mendelevium(258)

102No

Nobelium(259)

103Lr

Lawrencium(262)

1995 IUPAC masses and Approved Names from http://www.chem.qmw.ac.uk/iupac/AtWt/masses for 107-111 from C&EN, March 13, 1995, p. 35112 from http://www.gsi.de/z112e.html

Use the periodic table to learn electron configuration.

• There are many ways to use a periodic table to learn electron configuration.• Choose a periodic table that's uncluttered and easy to read.• Choose a method that works for you

1s

2s

3s

4s

5s

6s

7s

3d

4d

5d

6d

2p

3p

4p

5p

6p

4f

5f

• Here’s a periodic table broken into segments depicting the orbitals being filled in each subsection of the table


The Latest Periodic Table

• Here’s the latest version of the periodic table• Use this version to practice writing the electron configurations of the heaviest elements.

• Here’s another chart created from a periodic table.• It inserts the rare earth elements into the d-block, to

show the order in which orbitals are filled.


A Memory Device for Writing Electron Configurations

• Write orbitals with the same n on one line• Draw an arrow diagonally upward to the left through each

orbital symbol• Read the order by following the arrow bottom to top.

7s 7p 6s 6p 6d5s 5p 5d 5f4s 4p 4d 4f3s 3p 3d2s 2p1s

Some special electron configurations are very stable.

• Half-filled sets of p, d, and f orbitals are very stable.

• Completely-filled sets of d orbitals are very stable.

• They sometimes break the normal order of orbital filling.

• Recall Hund's rule: if electrons are filling orbitals in the same subshell, they don't pair up, but rather they spread out.

Gd 1s22s22p63s23p64s23d104p65s24d105p66s24f75d1

• Start with the configuration for the neutral atom, then add or remove electrons from the valence shells to make the desired ion.

Na atom 1s22s22p63s1

Na+ ion 1s22s22p6

• Atoms or ions that are isoelectronicif they have identical numbers and configurations of electrons.

Na+ 1s22s22p6

Ne 1s22s22p6

Electron configurations of ions don't include electrons that were lost, but they do include electrons that were gained.

With electron configurations of the outer electrons, we can discuss chemical reactivity and chemical bonding

• The electrons in the outermost shell are called valence electrons.

• In general, only valence electrons are important for chemical bonding.

Documents

Electronic Structure III. Quantum Numbers, Electronic ......•The principal quantum number, n, is a positive integer that indicates the shell and relative sizes and energies of orbital(s)