quantum numbers and atomic orbitals - chemistry 7 numbers and atomic orbitals each electron in an...
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Quantum Numbers and Atomic Orbitals
Each electron in an atom can be described by 4
quantum numbers: n, l, ml, ms.
An orbital describes a region in space where an
electron is most probably located.
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Name Symbol Permitted Values Property
Principal n Positive integers Orbital
energy (size)
Angular
momentum
l Integers from 0 to
n-1
Orbital shape
(s/p/d/f)
Magnetic ml Integers from -l
to 0 to +l
Orbital
orientation in
space
Spin ms +1/2 or -1/2 Direction of
e- spin
A shell describes electrons with the
same value of n. A subshell refers to
specific n,l quantum number (example:
2s subshell, or 3p subshell).
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size shape orientation
Learning Check
What is wrong with the following quantum
number designations and/or sublevel names?
Supply the missing quantum numbers and
sublevel names.
4
n l ml Name
(a) 1 1 0 1p
(b) 4 3 +1 4d
(c) 3 1 -2 3p
If n=1, only l=0 exists
l=3 is an f sublevel
If l=1, ml cannot be -2
n l ml Name
(a) ? ? 0 4p
(b) 2 1 0 ?
(c) ? ? ? 2s
Special Case of the H Atom
The energy state of the H atom depends
only on the principal quantum number n.
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Outline
1. Characteristics of Many-Electron Atoms
2. The Quantum-Mechanical Model and the
Periodic Table
3. Trends in Three Atomic Properties
4. Atomic Structure and Chemical Reactivity
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Excluded Topics:
• Trends among the transition elements
• Trends in electron affinity
• Pseudo-noble gas configuration
How does the distribution of electrons within the orbitals of an
element’s atoms relate to its chemical and physical properties?
Periodic Table
In 1870, Mendeleev arranged the 65
elements then known into a periodic table.
◦ Based on the periodic law: when the elements are
arranged in order of increasing atomic mass,
certain sets of chemical and physical properties
recur periodically
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Quantum Numbers and the
Exclusion Principle
Each electron in any atom is described
completely by a set of four quantum
numbers.
◦ The first three quantum numbers describe the
orbital, while the fourth quantum number
describes electron spin.
Pauli’s exclusion principle states that no
two electrons in the same atom can have the
same four quantum numbers.
An atomic orbital can hold a maximum of 2
e- and they must have opposing spins. 10 September 2013 9
Electronic Configuration
Distribution of electrons
within the orbitals
The lowest energy (ground
state) electronic
configuration of all elements
are constructed by filling
lowest energy orbitals
sequentially aufbau
principle
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Order of Filling the Orbitals
Memorize the order of filling orbitals! Use mnemonic device.
Recall: for an H atom, orbital energy depends on the quantum number n.
For many-electron atoms, orbital energy depends on both n and l (3s < 3p < 3d).
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spdf Notation and Orbital
Diagrams
Used to denote the ground state
electronic configuration of elements
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Element spdf
notation
Orbital box
diagram
H 1s1
He 1s2
n quantum #
l quantum #
# of e- in orbital
spin quantum
#: an arrow
denotes an
electron with
“spin up”
(ms=+1/2) or
“spin down”
(ms=-1/2)
Building Orbital Diagrams
1. Aufbau principle: electrons are always
placed in the lowest energy sublevel
available.
2. Exclusion principle: each orbital may
contain a maximum of 2 electrons, which
must have opposite spins.
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H (Z = 1) 1s1
1s
↑
He (Z = 2) 1s2
1s
↑↓
Building Orbital Diagrams
3. Hund’s rule: when orbitals of equal
energy are available, the lowest energy
electron configuration has the maximum
number of unpaired electrons with
parallel spins.
15
N (Z = 7) 1s22s22p3
Learning Check
Write a set of quantum numbers for the 3rd e- and a set for the 8th e- of the F atom.
Use the periodic table to identify the element with the electronic configuration 1s22s22p4. Write its orbital diagram.
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F (Z = 9) 1s22s22p3
For the 3rd electron: n = 2, l = 0, ml = 0, ms = +½
For the 8th electron: n = 2, l = 1, ml = -1, ms = -½
Partial Orbital Diagram and
Condensed Configurations
Partial orbital diagram: shows only the
highest energy sublevels being filled.
Condensed electron configuration: has
the element symbol of the previous
noble gas in square brackets
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Al (Z = 13) 1s22s22p63s23p1 ↑↓
3s 3p
↑
Al has the condensed configuration [Ne]3s23p1
Learning Check
Full Electron
Configuration
Element Condensed
Electron
Configuration
Partial
Orbital
Diagram
1s22s22p63s1 Na [Ne]3s1
1s22s22p63s2 Mg [Ne]3s2
1s22s22p63s23p4 S [Ne]3s23p4
1s22s22p63s23p4 Cl [Ne]3s23p5
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Electron Configuration and
Group
Elements in the same group:
◦ Have the same outer electron
configuration
◦ Exhibit similar chemical behavior
Similar outer electron
configurations correlate with
similar chemical behavior.
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Learning Check
Write the full and
condensed electron
configuration of the
following elements:
◦ Ca (20)
◦ Ti (22)
◦ Mn (25)
◦ Ni (28)
◦ As (33)
◦ Kr (36)
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Period 4 Elements
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*Colored type indicates the sublevel to which the last electron is added.
Period 4 Elements
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*Colored type indicates the sublevel to which the last electron is added.
Orbital Filling
and the Periodic Table
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The order in which the orbitals are filled can be obtained directly
from the periodic table.
Announcements Quiz # 7 on Sept 17.
LT # 3 on Sept 26 Th 6-7:30 PM, Venue TBA.
Chapter 8 Problem Set: 8, 10, 19, 20, 21, 23, 25,
27, 29, 30, 31, 32, 36, 41, 45, 47, 53, 56, 57, 59,
61, 64, 65
Problem Solving Class Schedule:
10 September 2013 24
Ch 7 D F 12:30 – 1:30 SOM 202
Ch 7 E F 11:30 – 12:30 CTC 102
Ch 7 F M 12:30 – 1:30 CTC 104
Ch 7 G W 2:30 – 3:30 SOM 105
Ch 7 H-K MWF 3:30 – 4:30 C 109
Ch 7 L T 4:30 – 5:30 C 114
Ch 7 C M 2:30-3:30 SOM 105