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The idea of the atom as being the irreducible constituent of matter is central
to our current understanding of
nature. According to Feynman, if there was one sentence that he
could communicate to a future civilization that has lost all
scientific knowledge, it would be the atomic hypothesis, namely that ``
all things are made of atoms - little particles that move around in perpetual
motion, attracting each other when they are a little distance apart, but
repelling upon being squeezed into one another''.
This single sentence contains the key to regaining almost
all of the current theories of science.
The ancients have conjectured that matter is made out of atoms for
many millennia. The word ``atom'' comes from the Greek word
``uncuttable'' coined by the Greek philosopher Democritus around
500 B.C. For the ancients, the atom was only an idea without
any material entity that could be identified as an atom, and without any
specific properties that could be empirical tested. For this reason, the Greek idea of the atom
cannot be taken to be a scientific hypothesis. In fact, comparing the statement of
Feynman regarding the atomic hypothesis with the Greek idea, we clearly see that the
formulation given by Feynman refers to material entities, and the properties of attraction
and repulsion are empirically verifiable properties. Hence, we can take the formulation of the
atomic hypothesis by Feynman to be a scientific hypothesis.
In contrast to Democritus, other Greek philosophers such as
Anaxagorus felt that matter consist of a layered structure, and that one
could never reach the final constituents of matter. Buddhist
philosophers, applying dialectical reasoning, came to the conclusion that
entities are composite, since any material entity can always be resolved into
dialectical opposites. They therefore concluded
that matter must be infinitely divisible, and cannot have any ultimate
Before one dismisses Anaxagorus and the Buddhists, one should note an irony of history
that, although the twentieth century
saw the vindication of the idea of the atom, nature seems more
like an onion, with one layer after another layer of substructure.
An even more radical challenge to the atomic hypothesis
is posed by string theory in which the ultimate constituents of nature are
not point like objects that we associate with an atom, but rather
extended objects such as strings, sheets, and from three to nine dimensional
structures, that are thought to be the smallest constituents of matter.
If matter is made out of continuous objects like a string, then we
are led to the view that matter is infinitely divisible, since
this is the property of any continuous body.
From the string point of view, the atom is just one of the many
layers in the organization of nature, and is only an effective description of
In the latter half of the eighteenth century, chemists returned to
the ancient idea of the atom. In studying how to combine different
materials, chemists found that there were two distinct forms of combination.
The first case was of a mixture
such that any amount of the two material could be
combined, such is the case in combining salt with water. The second the case was
of a chemical
reaction, where fixed proportions of two materials had to be
combined. For example, in dissolving copper in sulphuric acid, an
exact proportion of both material are needed, and an
excessive supply of, say, copper results in part of the copper
being left undissolved. Chemists then went on to conclude, by the early 1800's,
that there must be elementary constituents that were being combined in
chemical reactions, and finally came up with the idea of
irreducible elements, what we now know as atoms, and went
on to conclude that compounds - the present day term for which is
molecules - are made from the elements.
Physicists in the nineteenth century took up the idea of the atom
resulting from the study of heat and thermodynamics. They studied
how a gas behaves under different
pressure and temperature. The kinetic theory of gases was based on
the idea of a gas being composed out of large collection of atoms, and quantities such
as pressure and temperature were understood to result from the
properties of the atoms which composed the gas. The field of
statistical mechanics explained the phenomenon of heat and entropy
based on the idea that atoms compose all material entities.
By the end of the nineteenth century, the following questions were left unanswered:
what is the size of an
atom? how much does it weigh? and most importantly, what are the
laws that describe atomic phenomenon? As we have already
discussed briefly, the first great success of quantum mechanics was to
provide a complete theory to explain the existence, as well as the
properties, of atoms. In this chapter, we will complete the
discussion started with the Bohr atom, and show how the entire
Periodic Table of elements can be understood from the principles
of quantum mechanics.
A complete theoretical explanation for the existence of atoms comes from quantum theory.
Most of our ideas about atoms in general, including the most
complex ones, are based on our understanding of the hydrogen
atom (hydrogen atom), which is composed of a bound state of a single electron with a proton.
To understand the ingredients needed for a complete quantum
mechanical understanding of the atom, we revisit the Bohr atom to
understand its correct results as well as its shortcomings. The
key idea of Bohr, validated by later developments, is the
existence of pure numbers, called quantum numbers, that describe a
quantum state, and in particular, the atom.
dinger's equation gives the following
description of the hydrogen atom, and which has been verified to a very high degree of
accuracy by numerous experiments.
An atom is an electrically neutral object, and is composed of a
heavy, positively charged
nucleus, surrounded by an approximately equal number of negatively charged electrons.
Every proton has a charge equal in magnitude, but of opposite
sign, to that of an electron. The nucleus is made out of an equal number of protons and neutrons.
The nucleus has a size of about and is almost a million times smaller
than the size of the atom, which is about . The size of the electron is around
. Hence, in studying the atom, both the nucleus and the
electron can be considered to be point-like, and for example, the
Coulomb potential between the nucleus and the electrons is written
as if they were pointlike particles.
Protons and neutrons have a mass of
about , and an electron has a mass about 2,000 times
smaller, that is, about . (Recall is the energy gained by an
electron in moving across volt.) Since the nucleus of an
atom is about 4,000 times heavier than the electrons which
surround it, all the internal motion of an atom consists of
electrons moving around a nucleus that can be taken to be
stationary. For motion of the entire atom, all of its mass can be
taken to come from the nucleus.
the electrons of an atom, it is sufficient to impart to it energy of the
range of 1-100 eV. On the other hand, to excite the protons and neutrons
of the nucleus needs energy of the range of 5-100 MeV. Most phenomena
that we encounter in chemical,biological, thermal and
macroscopically observed processes involve energies of the range
of a only few eV's, the properties of an atom in this range of phenomena
results solely from
the behaviour of its electrons.
Consequently, we conclude that, given the large mass of the nucleus, and its high
excitation energy, the sole function of the
nucleus in an atom is to provide the atom with a pointlike mass and
positive charge, but is otherwise
taken to be inert. The only entity which is active in
ordinary circumstances are the electrons of the atoms,
and by the state of the atom is meant the state of the
electrons in the atom.
An atom is described by its wave function . For the case of the
hydrogen atom, the nucleus is considered to be at rest, with the electron
being bound to it by the electrostatic Coulomb potential. The
wave function determines the probability of the electron
being found a various distances from the nucleus.
Atoms and the Periodic Table
The electron in the atom has
angular momentum, and this is reflected in the wave function of the
electron. Although one cannot think that the electron
is "revolving" around the nucleus as a classical particle, a sense of angular
momentum is present in quantum mechanics. The electron in the atom has an average
a velocity, and hence, loosely speaking, in a bound state
is moving around the nucleus; hence it can have angular momentum. One should not take
this picture too literally, since the electron can have zero angular momentum in spite
of ``revolving'' around the nucleus, something that is not allowed by classical mechanics.
The higher the angular
momentum of the electron, the more likely that it is far from
the nucleus. Furthermore, angular momentum, just like energy and linear momentum, is
absolutely conserved in quantum mechanics.
An electron in an atom is fully described by four quantum numbers. They are
In sum, the wave function of the electron in an atom is described four quantum numbers, and is
symbolically represented by .
We briefly discuss below the physical significance of these quantum
Recall in our discussion on Bohr's model for the atom in Section 11.4, there
were two key formulae that underpin the Bohr atom, namely, that
the magnitude of the angular momentum of the atom is quantized, and which in turn leads
to the quantization of the energy of the electron in the atom.
Recall that we have, from eqs.(11.13) and (11.14) , that the energy of the
hydrogen atom is given by
- The principal quantum number that expresses the
quantization of energy, namely with
- The orbital quantum number
expresses the quantized values of the total
angular momentum of the electron in an atom, and has values
. The quantum number is said to be
angular momentum of the electron.
- Given that the angular momentum
of an electron is a vector quantity, quantum mechanics requires that
the angular momentum vector point in only discrete
directions. Choosing an arbitrary direction, say, the -axis, quantum
mechanics then dictates that the component of angular
take only certain discrete values, namely , where the integer
is the magnetic quantum number and is given by
- And finally, the theory of relativity requires that all
electrons have an intrinsic angular momentum, called spin, and denoted by vector
its -component , where is the spin quantum
and can take only two (2) values (along the -axis),
namely -1/2 and +1/2.
The most important success of the Bohr atom is the correct
prediction of the energy levels of the hydrogen atom. In fact, according to some authors,
the most important equation in atomic physics is the Bohr formula for the energy levels
of the hydrogen atoms. The principal quantum
number n expresses the discrete and quantum nature of the atom's
According to the Bohr atom, the lowest energy of the atom, called the ground
state, has . The higher the energy of the atom, the larger is the
value of , and the the further
away, on the average, is the electron from the nucleus. In the limit
, the (binding) energy of the electron in the atoms becomes zero,
and the electron becomes free from the nucleus. The energy levels of the hydrogen atom
are given in Figure 12.1. The process of
the electron gaining enough energy to escape
from its bound state (in an atom) is termed as ionization.
For example, the ionization of an electron in the ground state of
the hydrogen atom is .
The different values of can be represented by concentric
shells around the nucleus, with shells with larger values
having a larger radius. This shell structure of the hydrogen atom is
shown in Figure 12.2.
Energy Levels of the Hydrogen Atom
from eq.(11.1) that the energy of a photon with wavelength
is given by
The Shell Structure of the Hydrogen Atom
If an atom is subjected to radiation, it can absorb energy from photons. Suppose
the hydrogen atom is in an excited state denoted by and with energy , and that it
absorbs one quantum of photon by making a quantum transition to
a higher energy state with energy given by . From energy
conservation, we must have
and which yields
In other words, only certain wavelengths of light, given by above
formula can be absorbed (and re-emitted) by the hydrogen atom. Other wavelengths of
light will not be absorbed since this would entail a violation
of energy conservation. The spectrum of the hydrogen atom is given by
the wavelengths of light that are absorbed by it, and is illustrated in
Figure 12.3, with the inset being the spectral lines.
determine which frequencies an atom absorbs, we shine on it light containing a large range
of wavelengths. The electron in the atom absorbs only those wavelengths
of light allowed by eq.(12.8), and in doing so makes a quantum transition to a
higher energy level. The higher energy state is unstable, and
electron makes a transition to a lower energy state by re-radiating
the absorbed photon, which is then detected. Since only a discrete set of
wavelengths are absorbed, the radiation emitted by the atom has high intensity
for only a few select wavelengths, and these are called the spectral lines
for the atom in question.
Transitions from highly excited states
to the ground state are known as the Lyman series of spectral lines, and to
are called the Balmer series and so on. A typical wavelength
of the Lyman series has wavelength of
which is in UV range,
whereas for the Balmer series has wavelength of
which is in the violet range of the electromagnetic radiation.
The energy levels of
the hydrogen atom shown in Figure 11.1 have been reconstructed
from the study of the spectral lines of the hydrogen atom, and constitute
the biggest achievement of the Bohr atom. The energy levels of the hydrogen atom
responsible for the spectral lines of the hydrogen atoms are shown
in Figure 12.4.
The Absorption Spectrum of the Hydrogen Atom
There a number of problems with the Bohr atom.
Recall from eq.(11.10), that according to Bohr
the angular momentum of the hydrogen atom is given by
Spectral Lines of the Hydrogen Atom
The ground state of the hydrogen atom, given by ,
is experimentally determined, and has zero angular
momentum, contradicting the prediction of Bohr which requires it have a non-zero
value equal to . In fact, Bohr could not guess that angular momentum
needed a new quantum number, and had incorrectly identified
the quantum number for angular momentum with .
The correct result is obtained by solving Schr
and one obtains
that the magnitude of total angular momentum for the hydrogen atom, for a state
with energy , is given by
Quantum number denotes the orbital quantum number of the electron, and
reflects the angular momentum carried by the electron.
From the above formula, we immediately see that for the ground state of the hydrogen atom,
given by , has zero total angular momentum.
Recall angular momentum of the atom is a vector given by
The Heisenberg Uncertainty Principle implies that no experiment can fully
determine the value of all three components of angular
momentum L; all that experiments can determine is the
exact value of only one of them, say, . Since a component
cannot exceed the total magnitude of angular momentum, we have
and is shown in Figure 12.5 . is called the magnetic quantum
number as this is the component of angular momentum that couples
to an external magnetic field which can be taken to lie along the
Magnetic Quantum Number
The electron has intrinsic angular momentum called spin , which is a vector, and
has a fixed value. Note can point in only two
directions with values for
Due to the fact that
the projection of spin can take only two values, we can conclude
from eq.(12.12) that the spin has an angular momentum of
where is called the spin quantum number of the electron.
Hence the electron is said to be
a fundamental particle with spin .
general expression for angular momentum given in eq.(12.11),
the magnitude of spin angular momentum is given by
Spin up and down
Spin originates in the
theory of special relativity. The electron has intrinsic spin, and like its charge
and mass, is
an inherent property of the electron. All classical angular momentum is based on the idea
of a particle rotating about some axis; although electron spin
does have a sense of an axis as expressed by , in no sense
can one think of the electron as a classical spinning particle.
The electron itself is pointlike, and hence it cannot have any classical
angular momentum as this would need the electron to rotate about the point that it is
occupying, which is clearly not possible.
unlike all classical magnetic fields which are the result of the movement
of charge, due to its spin the electron carries a magnetic field even when it is not
in motion, and hence is an example of a quantum
mechanical source of magnetic fields without the motion of any charge.
Note that we have discussed the possible states that an electron
can have in a hydrogen atom, and found that to describe its wave function
we need four quantum numbers.
In discussing quantum numbers, for
brevity, one dispenses with writing the full wave function (which
contains the electron's probability distribution in space), and
instead one denotes the state simply by its quantum numbers,
Note that, once we fix , the
energy of all the states
with the allowed values of and is determined only by , and in
fact is given by the Bohr
In other words, the energy does not depend on the the quantum
numbers and . A situation such that many different quantum states,
specified by the various values of the quantum numbers , have
the same energy, is termed to be degenerate, and the
degeneracy is given by the number of states that have
the same energy.
We count the number of states of the hydrogen atom that have the same
energy by fixing , and then calculating how many different quantum
numbers correspond to a given .
Hence, the degeneracy of energy of the hydrogen atom is given by the
total number of states that have energy . Since, for a fixed , all
the states with different values of and have the same energy, by a simple
counting we have the degeneracy given by
- Quantum number =1,2,3......
- The quantum number takes values .
- The quantum number takes value for a given
- The spin quantum number has two values, regardless of the
value of .
In other words, for every allowed energy , or what is the same thing, for every
, there are states that have the same energy.
shell picture of the hydrogen atom, we now see that every shell has a
degeneracy of . This fact, in essence, contains the logical
kernel for explaining the entire
periodic table of elements, and has enormous importance in the
study of chemistry and biology.
We summarize the quantum numbers of an electron in the hydrogen atom in
Quantum Numbers of the Electron in the Hydrogen Atom
|Principal Quantum Number
|Orbital Quantum Number
|Magnetic Quantum Number
|Spin Quantum Number
|Total Degeneracy of Energy
The last ingredient we need for understanding the structure and stability of
atoms was formulated by Wolfgang Pauli, in 1925, and is called the
The exclusion principle states that, in
general, no two electrons can occupy exactly the same quantum
For the atom, the exclusion principle implies that if an
atom has more than two electrons, then no two electron can have
the wave functions with exactly the same set of
quantum numbers .
Example. Helium atom consists of a nucleus with two protons
and two neutrons, and two electrons bound to the nucleus. Suppose
the state of one of the electrons is in the lowest possible energy state
given by ; then
the second electron, due to the exclusion principle, cannot
be in the same state, and the best it can do to occupy the lowest
energy state available to be in the state . This
configuration of Helium's electrons is shown pictorially in Figure 12.7; the nucleus
is shown much larger than its actual size for indicating the number of protons
Note to the first box () in Figure 12.10
corresponds to Helium atom's electrons, with the electron's spin pointing in
opposite directions as required by the exclusion principle.
Helium Atom and Exclusion Principle
The Pauli exclusion principle was made on an ad hoc
basis, and it was only the later development of quantum
field theory that led to a more complete understanding. In
essence, the structure of spacetime, as dictated by the special
theory of relativity, allows only two kinds of fundamental
particles, called fermions and bosons.
Clearly, if the electron was a boson there would be no atoms as we know
since all the electrons would be in the lowest energy state corresponding to .
The exclusion principle is the reason for the elaborate structure of atoms,
is the basis of all of chemistry, and provides us with a principle for
organizing the multielectron system bound to the nucleus of an atom .
Recall an atom, in general, consists of number of protons with net positive charge
of and an approximately equal number of electrically neutral neutrons. (The number
of neutrons are larger than the number of protons for many nuclei, and isotopes
denote atoms whose nuclei does not have an equal number of protons and neutrons.)
The nucleus is surrounded by number of electrons
with a total electrical charge of , resulting in an electrically neutral atoms.
An atom is determined by the number of protons in the nucleus.
The number of stable atoms found in nature is about 90, and it is estimated that the maximum
number of atoms that can exist is 126. If one studies
the studies the physical and chemical properties of the various
atoms, a pattern is seen to emerge, wherein the physical and
chemical properties of the atoms seem to approximately
repeat themselves. The word ``periodic'' expresses this
repetitive (periodic) structure present in atoms.
- Fermions, which can have either spin , or at most spin ,
and obey the exclusion principle, in that no two fermions can
occupy the same state. The most familiar fermion is the electron,
followed by the proton, neutron and so on.
- Bosons have an integer spin of either or at most , and do
not obey the exclusion principle. In contrast, any number of bosons can all
occupy the same state. In particular, the equilibrium state for a collection
of bosons is for all them to occupy the lowest energy state, and leads to a
phenomenon known as boson condensation. The most familiar boson is the
photon, which has spin .
All macroscopic collection of atoms at room temperature are
either solid or gaseous, with the exception of mercury and
bromine that exist in the liquid state. All bulk material composed out of
a particular atom become solids at low enough temperature; in Figure 12.8
the atomic number of the atom is
plotted against its melting temperature. We can clearly see that
the temperature approximately repeats itself, and heavy vertical lines
have been drawn to mark this periodic behaviour.
There are numerous
other properties, such as ionization energy, density of atoms of a
particular kind, and so, also show a periodic pattern. This
pattern was recognized, in 1869, by Russian chemist Dmitri Medeleev,
who proposed the Periodic Table. At that time, many of the elements of the Periodic
Table had not yet been discovered, and Mendeleev made many
(successful) predictions of what the missing
elements should be, including properties such as atomic numbers and so on.
The predictive power of the Periodic Table is a canonical exemplar
of the scientific method, and illustrates the unique feature of the leading theories of
The periodic table of elements is given in Figure12.9. The
periodicity of the table is in the horizontal direction. The first problem
that needs to be addressed is why do atoms appear to have a periodic structure?
goes down vertically along any column, the atoms have similar
properties. This is the other outstanding feature of the periodic
table of elements that needs to be explained.
The Atomic Number Z Plotted Against the Melting Point of Atomic Material
The explanation offered by quantum mechanics for the structure of
atoms is the following. A crude first approximation to the multielectron system
of an atom is to
ignore the interactions amongst the electrons. We assume(incorreclty) that the
multielectron system is such that the electrons
interact only with the nucleus, and not with each other. With this approximation
we have a hydrogen-like situation, with the electrons being described by
wave functions of an electron in a hydrogen atom. Note the important
fact that, even for complex atoms with a high value of , the electrons are
described by the four quantum numbers ; however, the simple degeneracy of the hydrogen
atom no longer holds for more complex atoms.
In the approximation that we are considering, the energies of the
electrons are given by Bohr's expression for energy, with
the only difference
being that the charge of the proton in the hydrogen atom is replaced by , the charge of the
nucleus in question. Hence, from eqs.(12.3) and (12.4) , the energy of the
atom with nucleus having charge is given by replacing the
charge of the proton in the hydrogen atom by charge , and yields
The Periodic Table
Since electrons are fermions, the Pauli exclusion principle dictates that
they cannot all occupy the lowest energy
state of the atom. Hence, the electrons will arrange themselves into
successive shells, labeled by the principal quantum number .
Each shell can accommodate number of electrons, as these are
the number of states available in each shell. One can think of the
electronic configuration of an atom as being similar to a circular
amphitheater. The concentric energy shells correspond to
successive circles that have
increasing number of seats, and with the nucleus being the stage. As one goes
to atoms with larger and
larger number of electrons, the electrons arrange themselves in a
manner so as to occupy the seats in the shells closest to the stage.
When one shell is completed for some , all the
electronic states for that shell are occupied. This in particular
means that we have electrons with all values of quantum number
; hence the net projection of the value of
should be zero. A state with is spherically symmetric;
this means that other electrons will not be attracted to
this atom, and furthermore, this atom will not easily lose its
electrons. Atoms with a completely filled shell are the noble
gases (He, Ne, Ar, Kr, Xe and Rn) and signal the end of one of the
periods of the periodic table.
An example of the arrangement of electrons for the noble gas Neon is
given in Figure 12.10, with its 10 electrons distributed
in two energy shells given by and . The shell is
completely filled up, as is expected for a noble gas.
To sum up, the periods in the periodic table are the result of the
complete filling up of one of the shells of energy.
Since there are number of states available in the -th shell, we
should expect the periodic table to have the following periodicity
as shown in Table 12.2.
Arrangement of 10 Electrons in Two Shells for Neon
Expected and Observed Periodicity in the Periodic Table
|n th Energy Shell
|Number of atoms with period
|Observed number of atoms with period
We see from Table 12.2 that there are significant
deviations of the observed structure of the Periodic Table from
the prediction of the simple minded approximation that we have
considered. To get the actual structure of the periodic table by solving the
dinger's equation is even today an unsolved
problem, since it involves solving an intractable multielectron system.
However, without any detailed computation, we can qualitatively see where
the deviations from the simple picture based on the hydrogen atom starts
to take place.
In the simple approximations that we considered above,
we completely neglected the interactions amongst the electrons.
The electrons repel each other due to the Coulomb
potential. This leads to a removal of the degeneracy of states
that holds for the hydrogen atom, and, in general, the electrons in the atom depend
not only on the value of the quantum number , but start to
depend on quantum numbers as well.
Hence, instead of completely filling up one shell
before going on to the next, it may so happen that the high
angular momentum states for some value of ,
have a higher in energy than a low angular momentum state
belonging to the next -th shell.
This is in fact precisely what happens by the time one has reached
the shell. Neon is the noble gas that is the last
element of the shell, and, as expected, is inert and
unreactive. After Neon, we begin to populate the shell with the first
two atoms, namely, sodium and magnesium, and then followed by six
more elements (aluminum through argon). This accounts for the 8 atoms
in the shell. Following argon, we ``should'' be able to put
in 10 more elements according to the simple hydrogen-like counting
that we are doing. However, at this point, due to the interactions
of the electrons, and the fact that the electrons in the filled
shells start to ``shield'' - and effectively reduce - the charge of the
nucleus felt by the outer electrons. For this reason, both potassium and
choose to occupy the state as it has a lower energy than the
states of the previous shell.
One can imagine how intricate the actual structure of the atoms
become as one goes to larger and larger atoms with more and
The chemical and physical properties of
atoms are primarily determined by the number of electrons in their
outer most shell, since these are the electrons that are free to
interact with forces external to the atom. Hence, we expect atoms
with the same number of electrons in the outer shell to have
similar physical and chemical properties. This is the explanation
of why the elements in the vertical column of the periodic table
have similar properties.
Atoms with different atomic number , but with only one electron
in the outer shell, comprise the first column of the periodic
table, and are called the alkali metals (H, Li, Na, K, Rb, Cs,
Fr). All the alkali metals have
similar chemical properties, are highly reactive, and are easily
ionized. Figure 12.11 shows the electronic configuration of
Sodium (Na), with a single electron in the outer most
shell, called the valence electron.
Similarly, if two atoms are say one short of completely filling
up their outer most shell, they should be chemically similar. The halogens
(F, Cl, Br, I and At), comprising
the seventh column of the periodic table, are one electron short in filling up their
outer most shell, and all have similar chemical properties. An example of a halogen
is Chlorine (Cl) and its electronic configuration is shown in Figure 12.12.
mentioned, if an atom has a completely filled outer
shell, it will be inert belong to the noble gases.
Sodium as an Alkali Metal
In this way, all the elements of the periodic table can be
accommodated in the shell structure of atoms. The periodic
structure of the elements, as well as the similarity in their
chemical and physical properties, can be understood, both
qualitatively and quantitatively, from the principles of quantum
To empirically verify the energy levels and angular momentum
states occupied by the electrons of an arbitrary atom, the
spectral lines for the atom are determined in a manner similar to
the one discussed in the case of the hydrogen atom. The outer electrons of the atom experience
a shielded nucleus, since the electrons in the inner shells
partly cancel the positive charge
of the nucleus. Hence, the ionization and absorption spectrum of the outer electrons is in
of 1-20 eV and wavelength of respectively, similar to the hydrogen atom.
The noble gases have the maximum ionization potential, as is expected.
Note that the electrons in the inner shells experience the full unshielded charge
of the nucleus. Since the attractive
force is much larger in atoms with large , the binding energy goes as times
the binding energy of the hydrogen atom, as given in eq.(12.17). Hence, for
example, the spectral lines of a high atom such as molybdenum,
will have extra spectral lines due to absorption of radiation by the inner shell electrons
,in addition to the hydrogen like spectral lines due to the outer shell electrons.
For example, the Lyman lines for a high atom will have
wavelength shorter by a factor of . For , the wavelength is
, which is the wavelength in the X-ray range.
Chlorine as a Halogen
There are a number of different directions that one can go from the atom.
Atoms exert an attractive force on each other, and can form bonds resulting in the
formation of bound states of atoms,known as molecules.
There are two basic forms of bonds, namely the covalent and ionic bonds. The study
of molecules is the
subject matter of chemistry. Nature exhibits a bewildering variety of molecules, which
can have anything from a few to hundreds of atoms.
Macromolecules can have anything from thousands to millions of
atoms. Large macromolecules constitute the microscopic basis of life, and are the
subject matter of Molecular Biology. A typical protein is
a molecule resulting from the bonding of about 10,000 atoms; a DNA
molecule, the basis of all of life, can have anywhere from 50,000
to a few million atoms.
One can go in another direction, and take large aggregates of
atoms, and form bulk matter out of them. They can form exotic materials
such as semiconductors, superconductors, plastics, alloys and so on.
The study of materials, and of bulk matter in general, is the subject matter of
condensed matter physics as well as that of materials science.
X-ray scattering results for Molybdenum
The study of what composes the nucleus is the vast subject of nuclear physics, and focuses
on understanding the properties of nuclei starting from protons and neutrons.
The strong nuclear force binds the protons and neutrons to form
the nucleus. The proton and neutron in turn are seen to be composed out of
more fundamental particles called quarks. The nuclear force binds quarks
to form protons and neutrons.
The nuclear force field is called the gluon field. The gluon is force field similar
to the electromagnetic field, but far more complex
and counterintuitive. For example, the gluon field's attraction is
so strong that the quarks are permanently confined inside protons and neutrons, and can
never become a free particles such as, for example, the electron.
High energy physics studies the structure of quarks
and gluons, and has finally led to the idea of strings as the
underlying quantum of all of reality. Strings constitutes all of
physical reality, including all forms of matter, all force fields as well as the
geometry of spacetime.
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