does not need to be absorbed directly
by the reacting substances; it is possible, in photosensitization for example, that light can be absorbed by an
inert substance, which subsequently
transfers the absorbed energy (as
thermal energy) to the reactants.
ground state The lowest stable energy state of a system, such as a molecule, atom, or nucleus. See energy
level.
group 1. See periodic table. 2. A
mathematical structure consisting of
a set of elements A, B, C, etc., for
which there exists a law of composition, referred to as ‘multiplication’.
Any two elements can be combined
to give a ‘product’ AB.
(1) Every product of two elements is
an element of the set.
(2) The operation is associative, i.e.
A(BC) = (AB)C.
(3) The set has an element I, called
the identity element, such that IA =
AI = A for all A in the set.
(4) Each element of the set has an inverse A
–1 belonging to the set such
that AA
–1 = A
–1 A = I.
Although the law of combination is
called ‘multiplication’ this does not
necessarily have its usual meaning.
For example, the set of integers
forms a group if the law of composition is addition.
Two elements A, B of a group commute if AB = BA. If all the elements of
a group commute with each other
the group is said to be Abelian. If this
is not the case the group is said to be
non-Abelian.
The interest of group theory in
physics and chemistry is in analysing
symmetry. Discrete groups have a
Ünite number of elements, such as
the symmetries involved in rotations
and reÛections of molecules, which
give rise to point groups. Continuous
groups have an inÜnite number of elements where the elements are continuous. An example of a continuous
group is the set of rotations about a
Üxed axis. The rotation group thus
formed underlies the quantum
theory of angular momentum, which
has many applications to atoms and
nuclei.
group 0 elements See noble
gases.
group 1 elements A group of elements in the *periodic table:
lithium (Li), sodium (Na), potassium
(K), rubidium (Rb), caesium (Cs), and
Francium (Fr). They are known as the
*alkali metals. Formerly, they were
classiÜed in group I, which consisted
of two subgroups: group IA (the main
group) and group IB. Group IB consisted of the *coinage metals, copper,
silver, and gold, which comprise
group 11 and are usually considered
with the *transition elements.
group 2 elements A group of elements in the *periodic table: beryllium (Be), magnesium (Hg), calcium
(Ca), strontium (Sr), barium (Ba), and
radium (Ra). They are known as the
*alkaline-earth metals. Formerly,
they were classiÜed in group II,
which consisted of two subgroups:
group IIA (the main group, see alkaline-earth metals) and group IIB.
Group IIB consisted of the three metals zinc (Zn), cadmium (Cd), and mercury (Hg), which have two s-electrons
outside Ülled d-subshells. Moreover,
none of their compounds have
unÜlled d-levels, and the metals are
regarded as nontransition elements.
They now form group 12 and are
sometimes called the zinc group. Zinc
and cadmium are relatively electropositive metals, forming compounds containing divalent ions Zn
2+
or Cd
2+
. Mercury is more unreactive
and also unusual in forming mercury(I) compounds, which contain
the ion Hg 2
2+ .
253
group 2 elements
g
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by the reacting substances; it is possible, in photosensitization for example, that light can be absorbed by an
inert substance, which subsequently
transfers the absorbed energy (as
thermal energy) to the reactants.
ground state The lowest stable energy state of a system, such as a molecule, atom, or nucleus. See energy
level.
group 1. See periodic table. 2. A
mathematical structure consisting of
a set of elements A, B, C, etc., for
which there exists a law of composition, referred to as ‘multiplication’.
Any two elements can be combined
to give a ‘product’ AB.
(1) Every product of two elements is
an element of the set.
(2) The operation is associative, i.e.
A(BC) = (AB)C.
(3) The set has an element I, called
the identity element, such that IA =
AI = A for all A in the set.
(4) Each element of the set has an inverse A
–1 belonging to the set such
that AA
–1 = A
–1 A = I.
Although the law of combination is
called ‘multiplication’ this does not
necessarily have its usual meaning.
For example, the set of integers
forms a group if the law of composition is addition.
Two elements A, B of a group commute if AB = BA. If all the elements of
a group commute with each other
the group is said to be Abelian. If this
is not the case the group is said to be
non-Abelian.
The interest of group theory in
physics and chemistry is in analysing
symmetry. Discrete groups have a
Ünite number of elements, such as
the symmetries involved in rotations
and reÛections of molecules, which
give rise to point groups. Continuous
groups have an inÜnite number of elements where the elements are continuous. An example of a continuous
group is the set of rotations about a
Üxed axis. The rotation group thus
formed underlies the quantum
theory of angular momentum, which
has many applications to atoms and
nuclei.
group 0 elements See noble
gases.
group 1 elements A group of elements in the *periodic table:
lithium (Li), sodium (Na), potassium
(K), rubidium (Rb), caesium (Cs), and
Francium (Fr). They are known as the
*alkali metals. Formerly, they were
classiÜed in group I, which consisted
of two subgroups: group IA (the main
group) and group IB. Group IB consisted of the *coinage metals, copper,
silver, and gold, which comprise
group 11 and are usually considered
with the *transition elements.
group 2 elements A group of elements in the *periodic table: beryllium (Be), magnesium (Hg), calcium
(Ca), strontium (Sr), barium (Ba), and
radium (Ra). They are known as the
*alkaline-earth metals. Formerly,
they were classiÜed in group II,
which consisted of two subgroups:
group IIA (the main group, see alkaline-earth metals) and group IIB.
Group IIB consisted of the three metals zinc (Zn), cadmium (Cd), and mercury (Hg), which have two s-electrons
outside Ülled d-subshells. Moreover,
none of their compounds have
unÜlled d-levels, and the metals are
regarded as nontransition elements.
They now form group 12 and are
sometimes called the zinc group. Zinc
and cadmium are relatively electropositive metals, forming compounds containing divalent ions Zn
2+
or Cd
2+
. Mercury is more unreactive
and also unusual in forming mercury(I) compounds, which contain
the ion Hg 2
2+ .
253
group 2 elements
g
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