Dr. Saidane
Chem 200
Lecture Notes
Chapter 6, Part 2
Models of Atoms
Atomic Orbitals
In classical mechanics we speak of the path of electrons called orbits. However,
because of the wavelike properties of electrons we cannot say that an electron will be
found at a certain point in an atom. Ernest Shrödinger, an Austrian scientist, devised an
equation that describes electrons in terms of quantum mechanics. This equation lets us
calculate the probability that an electron is at a particular point in space, called orbital.
Each atomic orbital corresponds to an energy level of the electron. The higher the
energy, the larger the orbital. The various shapes of atomic orbitals can be classified into
four main types, which are labeled s, p, d, and f. There are many orbitals of each type.
They differ principally in the size of the cloud, which is related to the energy level.
The simplest way of drawing an atomic orbital is as a boundary surface, a surface within
which there is a high probability (typically 90%) of finding an electron.

An s-orbital has a spherical boundary surface, because the electron cloud is spherical.
s-orbitals with higher energies have spherical boundary surfaces of bigger diameter.

A p-orbital is a cloud with two lobes on opposite sides of the nucleus. The nucleus
lies on the plane that divides the two lobes, and an electron will, in fact never be
found at the nucleus itself if it is in a p-orbital. There are three p-orbitals of a given
energy, and they lie along three perpendicular axes.

The boundary surface of a d-orbital is more complicated than that of an s- or porbital. There are five d-orbitals of a given energy; four of them have four lobes, one
is slightly different and is oriented along an axis. In each case an electron that
occupies a d-orbital will not be found at the nucleus.

The f-orbitals have more complicated shapes. There are seven f-orbitals of a given
energy. The shapes of the f-orbitals are rarely needed to explain chemical properties
and therefore will not be studied here.
Quantum Numbers and Atomic Orbitals
Shrödinger found that each atomic orbital is identified by three numbers called quantum
numbers. One quantum number is called the principal quantum number, n; the other two
are the azimuthal quantum number, l, and the magnetic quantum number, ml. These
quantum numbers have another job: as well as labeling the orbital, they tell us about the
properties of the electron that occupies a given orbital.

The principal quantum number, n, is an integer that labels the energy levels around
the nucleus, from n =1 (ground state) to n = 7. Because the clouds representing the
orbitals get bigger as n increases, the average distance of an electron from the nucleus
also increases as n increases. On average, an electron is closest to the nucleus in the
ground state (n=1). The orbitals form a series of thick shells, sometimes like fuzzy
layers of an imaginary onion. Shells of higher n surround the inner shells of lower n.

The second quantum number, the azimuthal quantum number, l, governs the shape of
the orbital. Each value of l corresponds to one of the orbital shapes. Thus, l = 0
corresponds to s; l = 1, corresponds to p; l = 2 corresponds to d; l = 3 corresponds to f.
For each value of n, l can have the values between l = 0 and l = n-1. If n =1,then the
only value of l allowed is l = 0 (which corresponds to an s-orbital). When n = 2 , we
have two value of l, l = 0 (s-orbital) and l =1(p-obital). All the orbitals with a given
value of the azimuthal quantum number, l, are said to belong to the same subshell of
a given shell. Ex. The subshell 1s is the s-orbital for n =1.

The third quantum number, the magnetic quantum number, ml, labels the different
orbitals of a given subshell. The allowed values of ml are ml = l, l-1, l-2, …, -l. Ex
for the subshell with l =1, which consist of the p-orbitals, ml can have the values ml =
+1, 0, and –1, so there are three p-orbitals in the subshell. These orbitals are denoted
px, py, and pz. Each label corresponds to a possible orientation of the lobes of the
orbitals. In general, a subshell with quantum number l consists of 2l +1 individual
orbitals.
An orbital is specified by three quantum numbers; orbitals are organized into
shells and subshells.
The relations between shells, subshells, and orbitals are
summarized in the table below:
Quantum number, n, (shell)
Quantum number, l, (subshell)
Orbitals
1
0 (s-orbital), 1s
0
2
0 (s-orbital), 2s
0
1 (p-orbital), 2p
+1, 0, -1
0 (s-orbital), 3s
0
1 (p-orbital), 3p
+1, 0, -1
2 (d-orbital), 3d
+2, +1, 0, -1, -2
0 (s-orbital), 4s
0
1 (p-orbital), 4p
+1, 0, -1
2 (d-orbital), 4d
+2, +1, 0, -1, -2
3 (f-orbital), 4f
+3, +2, +1, 0, -1, -2, -3
3
4

Electron Spin. An electron behaves in some respect like a spinning sphere. It rotates
on its axis. This property is called spin. An electron has two spin states, represented
by the arrows  (for a clockwise rotation) and  (for a counterclockwise rotation).
These two spin states are distinguished by a fourth quantum number, the spin
magnetic quantum number, ms. This quantum number can have only two values: +1/2
indicates an  electron and –1/2 indicates a  electron.
Orbital Energies
As well as being attracted by the nucleus, each electron is repelled by all the other
electrons in the atoms. As a result, it is less tightly bound to the nucleus than it would be
if those electrons were absents. We say that each electron is shielded from the full
attraction of the nucleus by the other electrons in the atom. The shielding effectively
reduces the pull of the nucleus on an electron. The less shielding effect the closer the
electron is of the nucleus and the lower its energy level. An s-electron can be found close
to the nucleus and is said to penetrate through the inner shells. A p-electron penetrates
much less. For this reason, s-electrons lie at a lower energy than p-electrons of the same
shell. The order is s < p< d< f.
Orbitals in different subshells occupy different energy levels due to the shielding effect.
The order is as follows: 1s, 2s, 2p, 3s, 3p, etc...
The Electron Configuration or Building-up Principle of Atoms
We report the electronic structure of an atom by writing its electron configuration,
which is a list of all its occupied orbitals with the number of electrons that each contain.
In order to write the electron configuration of an atom we need to follows certain rules
and principles.
a) The Pauli exclusion principle (discovered and stated by the Austrian scientist
Wolfgang Pauli):

No more than two electrons may occupy any given orbital.

No two electrons in an atom can have the same set of four quantum numbers.
Which means that when two electrons do occupy one orbital their spin must be
paired. The spins of two electrons are paired if one is  and the other is .
b) The Aufbau principle gives the order in which atomic orbitals are occupied. Add the
Z electrons, one after the other, to the orbitals starting in the following order:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, etc…
c) Hund’s Rule (proposed by the German scientist Fritz Hund):
If more than one orbital in a subshell is available, add electrons with parallel spin to
different orbitals of that subshell rather than pairing two electrons in one of them.
Electron Configuration and the Periodic Table
The periodic table is an arrangement of the elements in order of their atomic
numbers so that elements with similar properties fall in the same column, or group.
Based on the electron configuration of the elements, the periodic table can be divided into
four blocks, the s, p, d, and f blocks.

The s-block elements: Groups 1 and 2.
a) The elements of group 1 of the periodic table are known as the alkali metals.
Their electron configuration ends with ns1, n being the period of the element and
1 is the number of valence electrons (outermost shell). Alkali metals are soft
shinny, and highly reactive.
b) The elements of group 2 are known as the alkaline-earth metals. Elements of
group 2 contain a pair of electrons in their outermost s subshell and therefore their
group electronic configuration ends with ns2. Alkaline earth metals are less
shinny, harder and less reactive than group 1 elements.

The p-block: Groups 13-18.
a) Elements in the p-block and in period 1 and 2, have an electron configuration that
ends with ns2np1-6.
b) For periods 3-7, the electron configuration ends with ns2(n-1)d1-10np1-6.
c) The properties of the elements in the p-block vary greatly, as the block includes
metals, non-metals, and metalloids.
d) The elements of group 17 are known as halogens. The elements of group 18 are
known as noble gases.

The p-block elements together with the s-block elements are called the main-group
elements or representative elements.

The d-block elements: Groups 3-12.
They have a configuration that ends with (n-1)d1-10ns2. The d-block elements are
metals with typical metallic properties and are often referred to as transition metals.

The f-block elements: Lanthanides and Actinides.
They have a configuration that ends with (n-2)f1-14(n-1)d1-10ns2.
a) There are 14 f-block elements between Lanthanum, La, and Hafnium, Hf, in the
sixth period called lanthanides (or rare earth elements). They are shiny metals
similar in reactivity to the group 2 alkaline-earth metals.
b) There are also 14 f-block elements, the actinides, between actinium, Ac, and
element 104, Unq, in the seventh period. They are all radioactive. The first four
are found naturally on earth.
The remaining actinides are laboratory-made
elements.
Skills you should have mastered
Conceptual
1. Distinguish and sketch the boundary surfaces of s-, p-, and d- orbitals.
2. Describe the interpretation of atomic orbitals in terms of probability.
3. Name and explain the relationship of each of the four quantum numbers to the
properties of electrons in orbitals.
4. List the allowed energy levels of a bound electron in terms of the quantum
numbers n, l, and ml.
5. State how many orbitals of each type are contained in the shell corresponding to a
given principal number and how many electrons can be accommodated in those
orbitals.
Problem-solving
1. Write the electron configuration for an element or ion.
Descriptive
1. Describe the general characteristics of elements in the s-, p-, and d- blocks.