Quantum Mechanical Model of the Atom

The model of the atom that we examined last day does not account for
the arrangement of electrons outside the nucleus.

Classical physics dictates that stationary, negatively charged electrons
should be pulled into the positively charged nucleus

In 1913 Niels Bohr proposed a model of the atom in which electrons are
arranged in concentric circular paths (orbits) around the nucleus;
patterned after the motion of the planets around the sun.

Bohr further went on to explain that electrons in particular orbits
possessed fixed amounts of energy.

The energy level of an electron is the region around the nucleus where it
is likely to be moving.

A quantum of energy is the amount of energy required to move an
electron from its present energy level to the next higher one.

The modern description of electrons in atoms is derived from solutions of
the Schrodinger equation, and is known as the quantum mechanical model.

Similar to the Bohr model, electrons are found in quantized energy levels,
however, the exact paths of the electons (the orbits) are not defined.
Instead, the location of an electron is defined in terms of probabilities
(the likelihood of finding an electron in a particular region of space).
Orbital: a region in an atom where the electron charge density, or the
probability of finding an electron, is high.

In the quantum mechanical model of the atom energy levels are
designated by the principal quantum number, n, and have values n = 1, 2, 3,
4, etc, where the energy of each level increases with increasing values of
n.
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The quantum mechanical model further divides each energy level into
sublevels, or orbitals.

Orbitals are given by both the principal quantum number (the energy
level), and the letter representing the sub-level (s, p, d, f, etc)
Nodes: region in which the probability of finding an electron is zero.
s-orbital: every energy level contains one s-orbital. An s-orbital is a
spherical region of space, centred at the nucleus, where there is a high
probability of finding an electron. An s-orbital can hold up to two electrons.
p-orbital: every energy level with n  2 contains 3 p-orbitals. A p-orbital is a
dumbbell-shaped region of space where there is a high probability of find an
electron. Each p-orbital can hold up to two electrons, hence for each energy
level, with n  2, a total of 6 electrons can be found in p-orbitals.
d-orbital: every energy level with n  3 contains 5 d-orbitals. Each d-orbital
can hold up to two electrons, hence for each energy level, with n  3, a total
of 10 electrons can be found in d-orbitals.
f-orbital: every energy level with n  4 contains 7 f-orbitals. Each f-orbital
can hold up to two electrons, hence for each energy level, with n  4, a total
of 14 electrons can be found in f-orbitals. To see a representation of forbitals visit: www.uky.edu/~holler/html/orbitals_2.html
Summary of Principal Energy Levels, Sublevels and Orbitals
Principal Energy
Level
Maximum Number
of Electrons
Allowed
Number of
Sublevels
Type of Sublevel
n=1
2
1
1s (1 orbital)
n=2
8
2
2s (1 orbital), 2p (3
orbitals)
n=3
18
3
3s (1 orbital), 3p (3
orbitals), 3d (5
orbitals)
n=4
32
4
4s (1 orbital), 4p (3
orbitals), 4d (5
orbitals), 4f (7
orbitals)
Electron Configuration

The way in which the electrons are arranged around the nucleus is the
electron configuration.

The way the electrons fill atomic orbitals (attain their electron
configuration) is dictated by three rules.
1. The Aufbau Principle: Electrons enter orbital of lower energy first.
Within an energy level, the s-orbital is always of lowest energy. Sometimes
there is overlap of high energy orbitals in one energy level with low energy
orbital in the next energy level. The diagonal rule can be used to determine
filling order.
2. The Pauli Exclusion Principle: An atomic orbital may describe at most two
electrons. A quantum property of electrons is spin (clockwise or counter
clockwise). Electrons occupying the same orbital must have opposite spins.
3. Hund’s Rule: When electrons occupy orbital of equal energy, one electron
enters each orbital until all the orbitals contain one electron with parallel
spins.
Example - Electron Configuration for Some Selected Elements
Valence Electrons: electrons in the electronic shell of highest principal
quantum number. That is, electrons in the outermost shell.
PERIODIC TABLE
Structure of the Periodic Table

Elements in the Periodic Table are arranged according to increasing
atomic number.

The horizontal rows are called periods. There are seven periods on the
Periodic Table.

The vertical columns are called groups, or families. Elements in the same
group exhibit similar properties.

Group IA through VIIIA are called Main Group elements

Group IB through VIIIB are called Transition Metal elements

The two rows of elements placed below the main part of the table are
called Lanthanides and Actinides



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Groups IA are the Alkali Metals
Group IIA are the Alkaline Earth Metals
Groups VIIA are the Halogens
Group VIIIA are the Noble Gases

The electronic configuration of any element can be determined quickly by
using the Periodic Table, as illustrated below.

Each period number corresponds to the principal energy level.

The number of electrons in a partially filled sublevel can be determined
by counting from left to right across a sublevel.

For the transition metals, electrons are added to a d-orbital with a
principal quantum number one less than that of the period number.

For the lantanides and actinides, electrons are added to an f-orbital with
a principal quantum number two less than that of the period number.