OBJECTIVES
After you have finished this lesson you should understand and know
* the structure and importance of the Periodic Table.
* the original Shell Model of the atom.
* the chemical structure of animate and inanimate materials.
* the various states of matter.
* the Principle of Indistinguishability.
* the detailed shell structure of atoms.
When we look around us, we see a great diversity of animate and inanimate
phenomena, all of which are built from atoms in various arrangements. It is
remarkable that such a multitude is constructed from only 90 naturally occurring
atoms. What does 'naturally occurring' mean? It refers to elements that have
existed in the earth's environment since the earth was born. Some other elements
are known and have been made, but are not stable here on earth, although certain
extraterrestrial environments may be found in which they are stable. (Stability in
this context means not changing since the earth was created.) Actually, most of
the things we see are built from a few common atoms such as carbon, hydrogen,
oxygen, nitrogen, and sulfur, and metals such as iron, copper, chromium,
nickel, silver, and gold.
When did we start to get a complete picture of the range of elements to be
found? Information gradually built up until Mendeleev produced The Periodic
Table of Elements in the latter part of the nineteenth century. This table arranged
the elements according to their chemical properties and atomic weights. The
weights of the elements essentially increased both down the columns and across
the rows. The columns consisted of elements that had similar chemical
properties. In the first table there were certain gaps, but because of the
continuous variations of the properties, one could predict the chemical properties
of these missing elements, which were subsequently confirmed when the
elements were discovered. This by itself would have given remarkable importance
to the table, but even more profound insights were inspired by this classification
scheme. The size of the rows is not constant; they go 2, 8, 8, 18, 18, 32 - a sequence
that has a certain periodicity, hence the name Periodic Table. It was found that
the number of protons in the elements, defined to be the atomic number of the
elements, increased by one from column to column in the same row and the first
element of the next row had one more than the last element of the preceding row.
As the atoms of the elements were neutral, the number of protons had to
correspond to the number of electrons in each of the atoms. The electrons are
found on the outside of atoms and clearly are associated with its chemical
properties. In order to explain the above sequence of numbers related to both
chemical properties and atomic weights, the hypothesis of electron shells was
created. The names of the shells were K, L, M, N, O, P, and so on; the K shell has
2 electrons, the L and M shells 8 each, the N and O shells 18 each. The 'filledness'
of the shells corresponded to chemical properties of the elements. The filled shells
corresponded to atoms of the inert gases, so called because they did not seem to
react with anything, not even each other.
At the beginning of the twentieth century the whole question of chemical
reactions was enigmatic. If electrons are on the outside of atoms, why do atoms
ever join in a chemical reaction? Why doesnÕt electron-electron repulsion push all
atoms apart? The realization that inert gases had filled shells led to the idea that
this was a particularly stable state for atoms and thus that atoms would find it
favorable to attain such a state. Based on this, a theory of chemical bonding was
born. The stability gained, in other words potential energy1 lost, when an atom
could have a filled shell for some time by sharing electrons with other atoms could
be great enough to overcome the increase of potential energy caused by electron
repulsion. In extreme cases an atom could lose electrons completely to form
positive ions or capture electrons a hundred percent of the time to form negative
ions. The ions would then have exactly enough electrons to form filled shells. In
order to form a chemical bond, the positive ions would stick to the negative ions by
electrical attraction. This latter extreme case scenario described ionic bonds,
while the former described covalent chemical bonds. This theory of chemical
bonding was a remarkable achievement-a theory of chemical reactions. But why
did electrons form shells? We shall come back to this point later in the
commentary.
Atoms and molecules are very small compared to the structures we see with
our own eyes, without the aid of microscopes. Thus there is a very large number
of atoms and molecules in objects that we do see-approximately 10^23! As we shall
see, this has some bizarre statistical consequences. For instance, in one small
drop of ink there are approximately 10^23 molecules of ink. When we place an ink
drop in a bathtub of water and stir the bath vigorously we see the ink drop
gradually mixing and distributing itself all through the bath water until it is
uniformly distributed. Then each volume of the bath water has an equal amount
of ink in it. If the bath is big enough each cube of water 1 millimeter by 1
millimeter by 1 millimeter will have one molecule of ink in it. Expressed
formally one states that the ink-bath mixture has reached Statistical or Thermal
Equilibrium. As another example, in each breath we exhale or inhale there are
again approximately 10^23 atoms of oxygen. If we subdivide the volume of oxygen in
the earthÕs atmosphere into volumes that equal the volume of a breath we get
again approximately 10^23! Thus given enough time, the oxygen atoms originating
in a single breath will mix with the earthÕs atmosphere and reach statistical
equilibrium at which time there will be one such atom in each 'breath' of the
earthÕs atmosphere. Whenever a person inhales, they will take in one of these
oxygen atoms.
Think about this: Julius Caesar died a long time ago; at that moment he let
out a dying breath that has reached statistical equilibrium with the earth's
atmosphere. Thus each breath you or I take includes an oxygen atom from Julius
Caesar's dying gasp. Continuing in this macabre vein, consider what happens to
the bodies of dead animals or humans if they are not locked in airtight containers.
The bodies decompose, turning to carbon, calcium, carbon dioxide, water, and so
forth, all of which form a mixture with the earth's biosphere and in time reach
statistical equilibrium. Thus the bones, internal organs, and skin in your body
almost certainly contain atoms from people who are dead. Recycling at its most
extreme!
One is not only sharing with people of the past, but also with those who are
alive now. Molecules from the outside of our bodies are continuously escaping us,
as are molecules from inside that are contained in the breaths we exhale. These
atoms and molecules originating from us are exchanging with external and
internal atoms and molecules of people around us, producing an intimacy that we
are not usually aware of and is pretty indiscriminate! As an example consider
smell, both pleasant and unpleasant, though let us concentrate on a desirable
scent. The only way our noses can respond is for molecules of the scent to interact
with molecules inside our noses. Thus scent molecules must leave the body they
are on, travel through the air, and be absorbed by the inside of our noses, causing
a response that is delivered to our brain. In general, living systems are in a
constant state of flux with their surroundings, continually exchanging molecules
and atoms.
Animate systems (living systems) are actually quite exceptional when
considered from the basic laws of chemistry and physics, which were designed
traditionally with inanimate systems (non-living) in mind. When in thermal
equilibrium, inanimate systems tend to be in a state of maximum disorder, while
at the same time having the lowest potential energy possible. (The term
'maximum disorder' in this context refers to the arrangement of the molecules
and atoms.) In contrast the everyday equilibrium structure of living beings is far
from one of maximum disorder, and lots of energy is expended in maintaining
ordered structures. However, when the life mechanism fails (i.e., death occurs),
this maintaining energy is lost and disorder takes over, which is manifested in
the decomposition of the body. Probably it is this facility of using energy to
maintain order that differentiates living from non-living materials.
All matter can be classified into four categories
Solid____Liquid____Gas____Plasma
A solid is a rigid, ordered structure that resists shearing motion (trying to push
the top part of the solid one way while pushing the bottom part the other way); a
liquid is more disordered and does not resist shearing forces, though it strongly
resists compressing forces as does a solid; a gas is even more disordered and offers
low resistance to compressing forces. Solid, liquid, and gas are said to be different
phases or states of matter. Plasma is an abnormal state. It is highly ionized and
dense, as all or most of the electrons that were contained in the atoms making up
the plasma have been stripped away. Such matter is found naturally in stars and
can be made on earth in controlled environments.
The term Antimatter is well known, but not its definition. It is not 'anti' to
'matter' in all properties; in fact, antimatter is matter. The only property that
characterizes antimatter is that of charge. An antimatter electronÑcalled a
positronÑhas a positive charge, equal but opposite to that of the electron, and it
has exactly the same mass as an electron. An antimatter proton has exactly the
same mass as a proton, but a negative charge equal but opposite to that of a
proton. An antimatter neutron is identical to any neutron as a neutron has no
charge! Why is antimatter called 'anti' matter then? The reason lies in the
observation that if a particle and its antiparticle (if they are different) collide,
they annihilate each other and form electromagnetic radiation, which is not
considered to be matter as it has no mass. Anti-atoms could exist, as well as
antiplanets and antistars, having basically the same properties as normal atoms,
planets, and stars. In fact it is possible that some of the stars we see in the night
sky are constructed of antimatter. However, if the two forms of matter ever came in
contact there would be a terrible gigantic explosion in which they would annihilate
each other in blinding flashes of light.
Let us once again delve into the strange realm of microscopic particles and
consider the process of measuring and observing. As you look around yourself in
this room, you can see objects and maybe people that you can identify and assign
names to. As we discussed in Lesson 2, this process of observation utilizes a
microscopic probe (photons) to interact with macroscopic objects, and the probe's
effect on the object is insignificant. In order to observe electrons, however, we
must use a microscopic probe to observe a microscopic particle, but the effects are
not insignificant and uncertainties are introduced. In particular there could be
uncertainties in the position of the electrons being observed. Remember one can
only determine the position within one wavelength of the incident probe, which
could be quite large compared to the 'size' of an electron. If one is observing a
group of electrons, many of the electrons would in general fit inside a wavelength
of the probe; if the wavelength of the probe is decreased, its energy increases and
hence also its disturbing effects, resulting in increased uncertainty of the position of
the electrons after the observation. It thus turns out that it isimpossible to track an
individual electron in a group of electrons; one can never be certain which of the
electrons in the group one is observing.
Recalling the Principle of Reality discussed in Lesson 2-if it is impossible to
measure or observe the described event, then this event cannot be an element of
physical realityÑone must conclude that electrons in groups of electrons cannot
have individual identities. This is called The Principle of Indistinguishability,
which applies to groups of all 'identical' microscopic particles (i.e., groups of
photons or groups of protons, etc.). The property of indistinguishability manifests
itself in two ways and is used to classify microscopic particles such as electrons,
protons, neutrons, photons, and so forth, into two families. One family is called
fermions, the other bosons; electrons, protons, and neutrons are fermions, while
photons are bosons. Fermions have the property that identical fermions cannot be
in the same place at the same time. This is called the Pauli Exclusion Principle.
This is not, however, true for bosons!
It turns out that there are two types of electrons. One can be thought of as
spinning clockwise, while the other spinning counterclockwise; one is called an
alpha electron, while the other a beta electron. Alpha and beta electrons can be at
the same place at the same time as they are not identical! Electrons are trapped
around nuclei by electromagnetic attraction and thus form atoms. Utilizing the
property of indistinguishability and the fact that electrons are fermions, one can
refine the original shell model of the atom and explain why electrons must form
shells. Electrons form subshells, which are regions of space that can
simultaneously contain two electrons-one alpha and one beta. These electrons
are not at the same place at the same time all the time, but they have the
possibility of being so sometimes. The first subshell is denoted by 1s and
corresponds to the K shell. This region of space is occupied by electrons in
preference to other regions as electrons in this region have the lowest energy,
thus this subshell is said to have the lowest energy. The second subshell is
denoted 2s, followed by 2px, 2py, and 2pz. The energy of the 2s subshell is higher
than the 1s, but lower than the 2px, 2py, and 2pz ones, which are equal to each
other. Subshells that have equal energy are said to be degenerate. As the electrons
are fermions, the 1s shell is filled when it contains two electrons, as is the 2s.
As each subshell is filled electrons start to fill the subshell that has the next lowest
energy. The number of electrons in a subshell is signified by asuperscript, thus the
arrangement in hydrogen is denoted by 1s1 and that in helium by 1s2. These symbols are
called the electronic configuration of the atom. Thus the electronic configuration of
lithium, which has atomic number three, is 1s22s2, and for beryllium (atomic number
four) it is 1s22s2. If subshells are degenerate, electrons prefer to arrange themselves
so that they are in different regions of space with the same spins if it is possible.
Thus nitrogen, which has seven electrons, has the electronic configuration 1s2s2p2p2p.
The subshells 2s, 2px, 2py and 2pz form the old L shell. Filled subshells are morestable
than unfilled ones unless they are degenerate like the 2p ones. In the followingtable we
summarize the correspondence between shells, subshells, and atoms. (Note thatthe 2p
shell is filled in accordance with the 'rules' we have just discussed.)
The formation and spatial properties of covalent chemical bonds can be explained in
terms of overlap of subshells between different atoms that need to share electrons in
order to produce closed subshells.
We now have a theory that explains why electrons are found at differentdistances and
in different regions of space surrounding the nucleus instead of all being concentrated
in one region. The old shell model just assumed this without explanation, but we are
still left with the nagging question of why the electrons fill the regions of space
that they do.