Transcript Electron Configurations

Chemistry: Atoms First
Julia Burdge & Jason Overby
Chapter 3
Quantum Theory and
the Electronic
Structure of Atoms
Kent L. McCorkle
Cosumnes River College
Sacramento, CA
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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Quantum Theory and the Electronic Structure of
Atoms
3.7 Quantum Numbers
Principal Quantum Number (n)
Angular Momentum Quantum Number (l)
Magnetic Quantum Number (ml)
Electron Spin Quantum Number (ms)
3.8 Atomic Orbitals
s Orbitals
p Orbitals
d Orbitals and other High-Energy Orbitals
Energies of Orbitals
3.9 Electron Configuration
Energies of Atomic Orbitals in Many-Electron Systems
The Pauli Exclusion Principle
Aufbau Principle
Hund’s Rule
General Rules for Writing Electron Configurations
3.10 Electron Configurations and the Periodic Table
Quantum Mechanics
Erwin Schrödinger derived a complex mathematical formula to
incorporate the wave and particle characteristics of electrons.
Wave behavior is described with the wave function ψ.
The probability of finding an
electron in a certain area of
space is proportional to ψ2 and
is called electron density.
Quantum Mechanics
The Schrödinger equation specifies
possible energy states an electron can
occupy in a hydrogen atom.
The energy states and wave functions
are characterized by a set of quantum
numbers.
Instead of referring to orbits as in the
Bohr model, quantum numbers and
wave functions describe atomic orbitals.
3.7 Quantum Numbers
Quantum numbers are required to describe the distribution of
electron density in an atom.
There are three quantum numbers necessary to describe an atomic
orbital.
 The principal quantum number (n) – designates size
 The angular moment quantum number (l) – describes shape
 The magnetic quantum number (ml) – specifies orientation
Quantum Numbers
The principal quantum number (n) designates the size of the
orbital.
Larger values of n correspond to larger orbitals.
The allowed values of n are integral numbers: 1, 2, 3 and so forth.
The value of n corresponds to the value of n in Bohr’s model of the
hydrogen atom.
A collection of orbitals with the same value of n is frequently called
a shell.
Quantum Numbers
The angular moment quantum number (l) describes the shape of
the orbital.
The values of l are integers that depend on the value of the
principal quantum number
The allowed values of l range from 0 to n – 1.
 Example: If n = 2, l can be 0 or 1.
l
0
1
2
3
Orbital designation
s
p
d
f
A collection of orbitals with the same value of n and l is referred to
as a subshell.
Quantum Numbers
The magnetic quantum number (ml) describes the orientation of
the orbital in space.
The values of ml are integers that depend on the value of the
angular moment quantum number:
– l,…0,…+l
Quantum Numbers
Quantum numbers designate shells, subshells, and orbitals.
Worked Example 3.8
What are the possible values for the magnetic quantum number (ml) when the
principal quantum number (n) is 3 and the angular quantum number (l) is 1?
Strategy Recall that the possible values of ml depend on the value of l, not on
the value of n.
Setup The possible values of ml are – l,…0,…+l.
Solution The possible values of ml are -1, 0, and +1.
Think About It Consult Table 3.2 to make sure your answer is correct. Table 3.2
confirms that it is the value of l, not the value of n, that determines the possible
values of ml.
Quantum Numbers
The electron spin quantum number (ms ) is used to specify an
electron’s spin.
There are two possible directions of
spin.
Allowed values of ms are +½ and −½.
Quantum Numbers
A beam of atoms is split by a magnetic field.
Statistically, half of the electrons spin clockwise, the other half spin
counterclockwise.
Quantum Numbers
To summarize quantum numbers:
principal (n) – size
angular (l) – shape
Required to describe an atomic orbital
magnetic (ml) – orientation
principal (n = 2)
2px
related to the magnetic
quantum number (ml )
angular momentum (l = 1)
electron spin (ms) direction of spin
Required to describe an
electron in an atomic orbital
3.8
Atomic Orbitals
All s orbitals are spherical in shape but differ in size:
1s < 2s < 3s
principal quantum
number (n = 2)
2s
angular momentum
quantum number (l = 0)
ml = 0; only 1 orientation
possible
Atomic Orbitals
The p orbitals:
Three orientations:
l = 1 (as required for a p orbital)
ml = –1, 0, +1
Atomic Orbitals
The d orbitals:
Five orientations:
l = 2 (as required for a d orbital)
ml = –2, –1, 0, +1, +2
Energies of Orbitals
The energies of orbitals in the hydrogen atom depend only on the
principal quantum number.
3s subshell
3;
l = 0)
3rd shell (n
(n ==3p
3)subshell
(n3d
= subshell
3; l = 1) (n = 3; l = 2)
2s
2ndsubshell
shell (n = 2)2p subshell (n = 2; l = 1)
(n = 2; l = 0)
Worked Example 3.9
List the Think
values of
n, l, and
ml for each
the orbitals
in a to
4dverify
subshell.
About
It Consult
theoffollowing
figure
your
answers.
Strategy Consider the significance of the number and the letter in the 4d
designation and determine the values of n and l. There are multiple values for ml,
which will have to be deduced from the value of l.
Setup The integer at the beginning of the orbital designation is the principal
quantum number (n). The letter in an orbital designation gives the value of the
angular momentum quantum number (l). The magnetic quantum number (ml) can
have integral values of – l,…0,…+l.
Solution
principal quantum
number, n = 4
4d
angular momentum
quantum number, l = 2
Possible ml are -2, -1, 0, +1, +2.
3.9
Electron Configurations
The electron configuration describes how the electrons are
distributed in the various atomic orbitals.
In a ground state hydrogen atom, the electron is found in the 1s
orbital.
Ground state electron
configuration of hydrogen
Energy
principal (n = 1)
2s
1s
2p
2p
2p
1
1s
number of electrons in
the orbital or subshell
angular momentum (l = 0)
The use of an up arrow indicates an electron
with ms = + ½
Electron Configurations
If hydrogen’s electron is found in a higher energy orbital, the atom
is in an excited state.
A possible excited state electron
configuration of hydrogen
Energy
2s
2s
1s
2p
2p
2p
1
Electron Configurations
In a multi-electron atoms, the energies of the atomic orbitals are split.
Splitting of energy levels refers to
the splitting of a shell (n=3) into
subshells of different energies
(3s, 3p, 3d)
Electron Configurations
According to the Pauli exclusion principle, no two electrons in an
atom can have the same four quantum numbers.
The ground state electron
configuration of helium
Energy
2p
2p
2p
1s
2s
2
Quantum number
Principal (n)
1s
describes the 1s orbital
Angular moment (l)
Magnetic (ml)
describes the electrons in the 1s orbital
Electron spin (ms)
1
0
0
+½
1
0
0
‒½
Electron Configurations
The Aufbau principle states that electrons are added to the lowest
energy orbitals first before moving to higher energy orbitals.
Li has a total of 3 electrons
The ground state electron
configuration of Li
Energy
2p
2s
1s
2p
2p
1s22s1
The third electron must go in the
next available orbital with the
lowest possible energy.
The 1s orbital can only accommodate 2
electrons (Pauli exclusion principle)
Electron Configurations
The Aufbau principle states that electrons are added to the lowest
energy orbitals first before moving to higher energy orbitals.
Be has a total of 4 electrons
The ground state electron
configuration of Be
Energy
2p
2s
1s
2p
2p
1s22s2
Electron Configurations
The Aufbau principle states that electrons are added to the lowest
energy orbitals first before moving to higher energy orbitals.
B has a total of 5 electrons
The ground state electron
configuration of B
Energy
2p
2s
1s
2p
2p
1s 2s 2p
2
2
1
Electron Configurations
According to Hund’s rule, the most stable arrangement of electrons
is the one in which the number of electrons with the same spin is
maximized.
C has a total of 6 electrons
The ground state electron
configuration of C
1s22s22p2
Energy
2p
2p
2p
2s
The 2p orbitals are of equal energy, or degenerate.
1s
Put 1 electron in each before pairing (Hund’s rule).
Electron Configurations
According to Hund’s rule, the most stable arrangement of electrons
is the one in which the number of electrons with the same spin is
maximized.
N has a total of 7 electrons
The ground state electron
configuration of N
1s22s22p3
Energy
2p
2p
2p
2s
The 2p orbitals are of equal energy, or degenerate.
1s
Put 1 electron in each before pairing (Hund’s rule).
Electron Configurations
According to Hund’s rule, the most stable arrangement of electrons
is the one in which the number of electrons with the same spin is
maximized.
O has a total of 8 electrons
The ground state electron
configuration of O
1s22s22p4
Energy
2p
2s
1s
2p
2p
Once all the 2p orbitals are singly occupied, additional
electrons will have to pair with those already in the
orbitals.
Electron Configurations
According to Hund’s rule, the most stable arrangement of electrons
is the one in which the number of electrons with the same spin is
maximized.
F has a total of 9 electrons
The ground state electron
configuration of F
1s22s22p5
Energy
2p
2s
1s
2p
2p
When there are one or more unpaired electrons, as
in the case of oxygen and fluorine, the atom is
called paramagnetic.
Electron Configurations
According to Hund’s rule, the most stable arrangement of electrons
is the one in which the number of electrons with the same spin is
maximized.
Ne has a total of 10 electrons
The ground state electron
configuration of Ne
1s22s22p6
Energy
2p
2s
1s
2p
2p
When all of the electrons in an atom are paired, as
in neon, it is called diamagnetic.
Electron Configurations
General rules for writing electron
configurations:
1) Electrons will reside in the available
orbitals of the lowest possible energy.
2) Each orbital can accommodate a
maximum of two electrons.
3) Electrons will not pair in degenerate
orbitals if an empty orbital is available.
4) Orbitals will fill in the order indicated
in the figure.
Worked Example 3.10
Write the electron configuration and give the orbital diagram of a calcium (Ca)
atom (Z = 20).
Setup Because Z = 20, Ca has 20 electrons. They will
fill in according to the diagram at right. Each s subshell
can contain a maximum of two electrons, whereas each p
subshell can contain a maximum of six electrons.
Solution
Ca 1s22s22p63s23p64s2
1s2 2s2
2p6
3s2
3p6
4s2
Think About It Look at the figure again to make sure you have filled the
orbitals in the right order and that the sum of electrons is 20. Remember
that the 4s orbital fills before the 3d orbitals.
3.10
Electron Configurations and the Periodic Table
The electron configurations of all elements except hydrogen and
helium can be represented using a noble gas core.
The electron configuration of potassium (Z = 19) is
1s22s22p63s23p64s1.
Because 1s22s22p63s23p6 is the electron configuration of argon, we
can simplify potassium’s to [Ar]4s1.
The ground state electron configuration of K:
1s22s22p63s23p64s1
[Ar]
[Ar]4s1
Electron Configurations and the Periodic Table
Elements in Group 3B through Group 1B are the transition metals.
Electron Configurations and the Periodic Table
Following lanthanum (La), there is a gap where the lanthanide
(rare earth) series belongs.
Electron Configurations and the Periodic Table
After actinum (Ac) comes the actinide series.
Electron Configurations and the Periodic Table
Electron Configurations and the Periodic Table
There are several notable exceptions to the order of electron filling
for some of the transition metals.
 Chromium (Z = 24) is [Ar]4s13d5 and not [Ar]4s23d4 as
expected.
 Copper (Z = 29) is [Ar]4s13d10 and not [Ar]4s23d9 as expected.
The reason for these anomalies is the slightly greater stability of d
subshells that are either half-filled (d5) or completely filled (d10).
Cr
[Ar]
4s
3d
3d
3d
3d
3d
Greater stability with half-filled
3d subshell
Electron Configurations and the Periodic Table
There are several notable exceptions to the order of electron filling
for some of the transition metals.
 Chromium (Z = 24) is [Ar]4s13d5 and not [Ar]4s23d4 as
expected.
 Copper (Z = 29) is [Ar]4s13d10 and not [Ar]4s23d9 as expected.
The reason for these anomalies is the slightly greater stability of d
subshells that are either half-filled (d5) or completely filled (d10).
Cu
[Ar]
4s
3d
3d
3d
3d
3d
Greater stability with filled 3d
subshell
Worked Example 3.11
Write the electron configuration for an arsenic atom (Z = 33) in the ground state.
Setup The noble gas core for As is [Ar], where Z = 18
for Ar.
The order of filling beyond the noble gas core is 4s, 3d,
and 4p. Fifteen electrons go into these subshells because
there are 33 – 18 = 15 electrons in As beyond its noble gas
core.
2
2
6
2
6
2
3
Solution
As
[Ar]4s23d104p3
Think About It Arsenic is a p-block element; therefore, we should
expect its outermost electrons to reside in a p subshell.
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