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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
principal quantum number
angular momentum quantum number l=0:
The size of an s orbital increases with n.
n=3, l=0
“s” orbital
principal quantum number
angular momentum quantum number l=0:
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
principal quantum number
angular momentum quantum number l=0:
Electrons p orbitals occupy opposite sides of the nucleus.
n=2, l=1
“p” orbital
principal quantum number
angular momentum quantum number l=1:
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
Electron configurations follow the organization of the periodic table.
Electron configurations follow the organization of the periodic table.
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
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
Use the periodic table to learn electron configuration.
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.
Use the periodic table to learn electron configuration.
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.