CHEMISTRY 4
CHAPTER 11
ATOMIC THEORY: THE QUANTUM MODEL OF THE ATOM
1 ELECTROMAGNETIC RADIATION
In one hand, light can be considered as an electromagnetic radiation characterized by its
velocity ( velocity in vacuum is 2.9979 x 10 8 m/s ) its wavelength  or frequency  .
On the other hand light can be considered as a stream of “particles” called photon , with
energy given by
E = h
When white light is passed through a prism, it produces a spectrum which contains all
wavelengths.
A spectrum that contains all the wavelengths is called continuous spectrum.
When the hydrogen emission spectrum is passed through a prism, we see only a few
lines, each of which corresponds to discrete wavelength. The hydrogen spectrum is
called a line spectrum. The line spectrum of hydrogen indicates that only certain energies
are allowed for the electron in the hydrogen atom.
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2 THE BOHR MODEL OF THE HYDROGEN ATOM
In 1913 Niels Bohr proposed that the electron in a hydrogen atom moves around the
nucleus only on certain allowed circular orbits and thus the energy of the electron in the
hydrogen atom is quantized. The Bohr model correctly explained the hydrogen spectrum,
but failed when it was applied to other atoms.
3 THE QUANTUM MECHANICAL MODEL OF THE ATOM.
In 1927 Werner Heisenberg derived the uncertainty principle, which states that it is
impossible to know simultaneously both the momentum (mv )and the position of a
particle with certainty. Therefore we cannot speak of the orbit of an electron around the
nucleus.
ORBITALS.
In 1926, Ervin Schrodinger advanced the famous wave equation that relates the energy of
a system to its wave properties.
H = E 
E is the energy of the atom, and  (x,y,z) is called the wave function. The Schrodinger
equation for the system of one electron and one nucleus can be solved exactly.
The wave function of one electron is called orbital. The square of the orbital () is a
direct measure of the probability density of finding the electron in that orbital at any
particular point. So it is usually most helpful to picture an orbital as a three-dimensional
electron density map. To represent the shape of electron density, it is convenient to use
surface of constant probability density. To describe the “size” of an orbital, it is common
to use a surface of constant probability density that encloses 90% of the electron density.
The region of space in which an electron is most likely to be found can be visualized
as the orbital itself. For many-electron atoms, the Schrodinger equation cannot be
solved exactly. Nevertheless, with some modification, the hydrogenlike orbitals can
account adequately for the electronic structure of many-electron atoms.
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Quantum number specification of orbital
Atomic orbital are specified by three orbital quantum numbers:
a) The principal quantum number n. n has integral values 1,2,3....
In a general way, the effective volume of an electron orbital depends on n. As n
increases, the orbital becomes larger and the electron spends more time further from the
nucleus and the electron is less tightly bound to the nucleus. Orbitals with the same
quantum number n are said to belong to the same shell. Each shell has n2 orbitals
b) The orbital shape quantum number l (also called the angular momentum
quantum number). For each value of n, l can have n integral values from 0 to n-1. This
quantum number is related to the shape of atomic orbitals. The value of l for a particular
orbital is commonly assigned a letter: l = 0 is called s (s-orbital has a spherical shape); l =
1 is called p (p-orbital has two lobes on opposite sides of the nucleus) ; l = 2 is called d
(orientation are shown in figure above); l = 3 is called f. Orbitals with the same quantum
numbers n and l are said to belong to the same subshell
c) The orbital orientation quantum number ml ( also called magnetic quantum
number) For a given value of l, ml can have (2l+1) integral values between l and -l,
including zero . Thus we have one orbital ns, three orbitals np, five orbitals nd, seven
orbital nf. In general ml determines the orientation of the orbital in space relative to a
reference axis which can be an external magnetic field.
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n
l
1
2
0
0
1
0
1
2
0
1
2
3
3
4
Atomic orbital
orbital
ml
designation
1s
0
2s
0
2p
-1, 0, 1
3s
0
3p
-1, 0 , 1
3d
-2, -1, 0, 1, 2
4s
0
4p
-1, 0, 1
4d
-2, -1, 0, 1, 2
4f
-3, -2, -1, 0, 1, 2, 3
number of
orbitals
1
1
3
1
3
5
1
3
5
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ORBITAL ENERGY
Orbital energy depends on quantum numbers n and l.
In many-electron atom, each electron is shielded from the nucleus
by the other electrons. In general energies increase as the quantum
number n increases.
Energy levels with the same principal quantum number n are said
to belong to a same principal level.
For each principal level there are one or more sublevels, which are
s, p, d, f... . Electron on orbital ns can penetrate closer to the
nucleus than electron on orbital np, thus s electron has lower energy
than p electron.
In general the order is ns< np < nd < nf
ELECTRON SPIN AND THE PAULI PRINCIPLE
Spectral data indicate that electron has a magnetic moment with two possible orientations
relative to an external magnetic field. Electron spin quantum number ms has been
introduced to describe the two spin states of the electron. Spin quantum number ms can
have only one of two values +1/2 and -1/2. The state of the electron is thus specified by
four quantum numbers : n, l, ml, and ms.
Pauli principle: In an atom no two electrons can have the same set of four quantum
number. Since electrons in the same orbital have the same values of n, l, ml they must
have different values of ms. Thus an orbital can only hold two electrons, and they must
have opposite spins. Therefore the maximum number of electrons in a sublevel l is twice
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the number of orbitals in the sublevel, 2 (2l+1). The maximum number of electrons on
level n is 2 n2
4 ELECTRON CONFIGURATION AND THE PERIODIC TABLE
For atom in the ground state (lowest energy) there are two rules that guide the
assignments of electrons to orbitals:
1) At ground state the electrons fill the lowest energy orbitals available.
2) No orbitals can have more than two electrons.
The total number of electrons at any sublevel is shown by a superscript number.
Using these rules we can find the electron configuration of atom at ground state.
Example 1 Find the electron configuration of hydrogen atom .
Hydrogen atom has one electron. This electron will occupy the lowest energy level 1s.
So the electron configuration of hydrogen is :
1s1
Example 2 Find the electron configuration of helium atom .
Helium has two electrons. Since two electrons with opposit spin can occupy an orbital ,
both electrons of helium will occupy the level 1s. So the electron configuration of helium
is :
1s 2
Example 3 Find the electron configuration of oxygen atom at ground state.
Oxygen atom has 8 electrons. Two electrons will occupy the orbital 1s, two electrons
will occupy the the orbital 2s, anf four electrons can occupy the three orbitals 2p. So the
electron configuration of oxygen atom should be :
1s22s22p4
Example 4 . Find the electron configuration of neon
The ten electrons of neon atom will occupy the orbitals 1s, 2s, 2p. The electron
configuration of neon will be :
1s22s22p6
This configuration is very stable
Example 5 Find the electron configuration of sodium.
The first ten electrons occupy the 1s, 2s, 2p orbitals and the eleventh electron must
occupy the first orbital with n = 3, the 3s orbital. The electron configuration of sodium is
:
1s22s22p63s1
To avoid writing the inner level electrons, this configuration is often abbreviated as
[Ne] 3s1, where the [Ne] represents the electron configuration of neon.
There is an important pattern in the way sublevels are filled in different regions of the
periodic table. In groups 1A,2A the s sublevels are the highest occupied energy
sublevels. The p orbitals are filled in order across groups 3A to 8A. The d orbitals are
filled in the B groups ( transition metals) The lanthanides correspond to the filling of the
seven 4f orbitals. The actinide series corresponds to the filling of the seven 5f orbitals.
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It is important to be able to give the electron configuration knowing the position of the
element in the periodic table.
Example 1 Give the electron configuration of sulfur.
Sulfur is element sixteen and resides in period 3, where the 3p orbitals are being filled.
Since sulfur belongs to group 4A, and is the fourth among the “3p elements”, it must
have four 3p electrons. Its configuration is :
1s22s22p63s23p4 or [Ne] 3s23p4
Example 2 Give the electron configuration of cadmium.
Cadmium is element 48 and is located in period 5 at the end of the 4d transition metals.
It is the tenth element in the series and thus has 10 electrons in the 4d orbitals. The
configuration is :
1s22s22p63s23p64s23d 10 4p65s24d10 or [Kr] 5s24d10
5 VALENCE ELECTRONS
Valence electrons are defined as electrons in the outermost principal quantum level of an
atom. The inner electrons are known as core electrons. The elements in a same group
have the same valence electron configuration. So the similar chemistry exhibited by the
members of a given group arises from the fact that they all have the same electron
configuration. only the principal quantum number of the valence orbitals changes in
going down a particular group. The group labels for main-groups 1A, 2A, 3A, 4A, 5A,
6A, 7A, and 8A indicate the total number of valence electrons for atoms in these groups.
For example all elements in group 7A have the configuration ns2 np5.
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6 TRENDS IN PERIODIC TABLE
Atomic size
Moving across the table from left to right, the atoms become smaller.
Moving down the table in any group, atoms ordinarily increase in size.
These observations are believed to be the result of three influences:
1) Highest occupied principal energy level
2) Nuclear charge
3) Shielding effect of nucleus charge by inner electrons
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Ionization energy.
Ionization energy is the energy required to
remove one electron from a neutral gaseous
atom.
The ionization energy decreases as the
atomic number increases within the group.
As the atomic number increases within a
period, the general trend in ionization energy
is an increase.
Metals and nonmetals
.
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