A seminar on Modern atomic Structure by bibin079


									                                                                                                                           Page |1


Although the word ‗atom‘ is borrowed from a Greek word which means indivisible, we know that that doesn‘t hold
true anymore about the atom. We now know the atom is composed of electrons, protons, and neutrons. Then
protons and neutrons are further made of quarks bonded by the strong interaction through force mediating
particles known as gluons.

Now how do we know all these?

The experts of this field, the particle physicists a.k.a. high-energy physicists, are able to determine the
constituents of tiny particles by smashing them together in gargantuan devices called particle accelerators and
colliders. Basically, the higher the energies these devices are able to generate, the more scientists can peer into
the particles‘ innards.

This year, 2009, particle physicists will be given the chance to peer even deeper when the largest collider ever
built goes operational. The Large Hadron Collider (LHC) at CERN will be capable of colliding two protons at
energies of 7 TeV each. No collider has come close to reaching these magnitudes.

One of the precursors of today‘s particle accelerators was the apparatus used by Ernest Rutherford in his popular
Gold Foil Experiment. By directing a beam of alpha particles to a gold foil and observing how they were scattered
after collision, Rutherford was able to refute JJ Thomson‘s earlier model of the atom.

This simple experiment, which allowed fast moving projectiles (the alpha particles) to collide with a steady target
(the gold foil) showed that atoms didn‘t have a plum pudding structure as suggested by Thomson but rather that it
(the atom) had a very dense positively charged core.

Simple devices like this later on evolved to larger and more sophisticated machines using higher energies.
What‘s more, the collisions no longer only involved projectiles and fixed targets. Instead, experiments in colliders
like the LHC bring two fast moving particles to head-on collisions. Subsequently, it allowed us to discover tinier
and tinier particles.

Using particle accelerators and colliders, we have found that the atom has an order of magnitude of 10                           m; the
            -14                                   -15                              -18                          -19
nucleus, 10       m; the neutron and proton, 10         m each; the electron, 10         m; and the quark, 10         m.
It‘s not only high-energy physicists who are interested in knowing what secrets lay hidden in even smaller orders
of magnitude. Astronomers, who are normally more concerned with structures of the largest scale are also
curious. Apparently, they believe a better understanding of the tiniest particles can provide valuable clues as to
how the Universe came into being.

A Timeline on Atomic Structure

400 B.C. Democritus‘ atomic theory posited that all matter is made up small indestructible units he called atoms.

1704     Isaac Newton theorized a mechanical universe with small, solid masses in motion.

1803    John Dalton proposed that elements consisted of atoms that were identical and had the same mass and
that compounds were atoms from different elements combined together.

1832     Michael Faraday developed the two laws of electrochemistry.
                                                                                                       Page |2

1859    J. Plucker built one of the first cathode-ray tubes.

1869    Dmitri Mendeleev created the periodic table.

1873 James Clerk Maxwell proposed the theory of electromagnetism and made the connection between light
and electromagnetic waves.

1874 G.J. Stoney theorized that electricity was comprised of negative particles he called electrons.

1879      Sir William Crookes‘ experiments with cathode-ray tubes led him to confirm the work of earlier scientists
by definitively demonstrating that cathode-rays have a negative charge.

1886     E. Goldstein discovered canal rays, which have a positive charge equal to an electron.

1895    Wilhelm Roentgen discovered x-rays.

1896    Henri Becquerel discovered radiation by studying the effects of x-rays on photographic film.

1897    J.J. Thomson determined the charge to mass ratio of electrons.

1898    Rutherford discovered alpha, beta, and gamma rays in radiation.

1898 Marie Sklodowska Curie discovered radium and polonium and coined the term radioactivity after studying
the decay process of uranium and thorium.

1900     Max Planck proposed the idea of quantization to explain how a hot, glowing object emitted light.

1900 Frederick Soddy came up with the term "isotope" to explain the unintentional breakdown of radioactive

1903 Hantaro Nagaoka proposed an atomic model called the Saturnian Model to describe the structure of an

1904     Richard Abegg found that inert gases have a ―stable electron configuration.‖

1906    Hans Geiger invented a device that could detect alpha particles.

1914    H.G.J. Moseley discovered that the number of protons in an element determines its atomic number.

1919    Francis William Aston used a mass spectrograph to identify 212 isotopes.

1922     Niels Bohr proposed an atomic structure theory that stated the outer orbit of an atom could hold more
electrons than the inner orbit.

1923    Louis de Broglie proposed that electrons have a wave/particle duality.

1929 Cockcroft / Walton created the first nuclear reaction, producing alpha particles

1930    Paul Dirac proposed the existence of anti-particles.

1932    James Chadwick discovered neutrons, particles whose mass was close to that of a proton.

1938    Lise Meitner, Hahn, Strassman discovered nuclear fission.

1941-51 Glenn Seaborg discovered eight transuranium elements.

1942     Enrico Fermi created the first man-made nuclear reactor.

Topics Covered under Atomic Structure Chemistry

        Introduction to Atomic Structure
                                                                                      Page |3

      Fundamental Particles
      Discovery of Electrons: Cathode Rays
      Determination of Velocity & charge/Mass ratio of electron
      Millikan’s Drop Method (Charge Determination in electron)
      Discovery of Proton: Positive Rays or Canal Rays
      Discovery of Neutron
      Atomic Terms
      Atomic Models
      Thomson’s Model
      Rutherford’s Model
      Alpha Scattering Experiment
      Defects in Rutherford’s Model
      Characteristics of Waves
      Electronic Magnetic Radiation
      Atomic Spectrum
      Planck’s Quantum Theory
      Bohr’s Atomic Model
      Hydrogen Atom: Radius and Energy Levels
      Calculation of Energy in Electron
      Quantum Numbers
      Pauli’s Exclusion Principle:
      Shapes and Size of Orbital
      Rules of filling Electrons in Orbitals
      Hund’s Rule of Maximum Multiplicity
      Electronic Configuration of Elements
      Derivation of de-Broglie Equation
      Relation Between Kinetic Energy and Wavelength
      Derivation of Angular Momentum from de Broglie Equation:
      Photoelectric Effect coduction to Atomic Structure

Structure of an Atom
An atom is composed of three different types of particles; protons, neutrons, and electrons.
Because atoms are neutrally charged, an atom will always have the same number of protons
and electrons. This idea that atoms are neutral is by definition. Atoms always have the same
number of negative and positive charges. By the way, atoms become ions when they become
charged. This change can occur when an atom has either lost or gained some electrons. So
                                          ions do not have the same number of protons and
                                          The example atom to the left or above, represents
                                          Helium which is usually a gas. Helium has 2
                                          protons, 2 neutrons, and 2 electrons. The protons
                                          and neutrons form the nucleus and the electrons
                                          form a cloud that surrounds the nucleus.
                                          Now what is it about this atom that makes it a
                                          Helium atom? It is the number of protons that
                                          determines what kind of element the atom will be.
                                          A Helium atom will always have 2 protons. If it is
                                          a non-charged atom, it will also have 2 electrons.
                                          There are; However, several varieties of Helium and
                                          they differ in the number of neutrons. Scientists call
                                                                                                         Page |4

these varieties isotopes. Most of the Helium that we breath in our air is Helium 4 which has
2 neutrons. There are also a small number of Helium 3 atoms in our air as well. Both of
these varieties of Helium are stable. They do not break down. So they are not radioactive.

Atom Symbols
                                   Above we were looking at an atom of Helium that had 2
                                   protons, 2 neutrons, and 2 electrons. Its called Helium 4.
                                   Now we will see the other symbols that are used to identify
                                   this kind of atom.
                                   The diagram to the left or above shows two common types
                                   of symbols. The Top symbol is just a shortened version of
                                   Helium 4. Most of the time the chemical names are not
                                   spelled out. Instead, the chemical symbol (He) is used. The
                                   number that follows the name or the symbol is the mass
                                   number. The mass number tells us which Helium isotope we
                                   are looking at by telling how many protons and neutrons are
                                   in the nucleus.
                                   If we look at a periodic table of the elements we see that
                                   Helium always has an atomic number of 2, which tells us
                                   that there are two protons in this atom. So we can subtract
                                   the Atomic number (2) from the mass number (4) to get 2
neutrons in He 4. The other symbol (on the graphic) already shows both the Mass number
and the Atomic number.
By the way, the Atomic Mass is not the same as the Mass Number. The Atomic Mass is an
average mass of naturally occurring isotopes that are found on the earth. If you have a
sample of Helium, the average mass would be 4.0026. Mass Number, on the other hand, is
the protons + neutrons of an atom. So do not confuse the two terms.

Fundamental Particles
According to the Standard Model, all elementary particles are either bosons or fermions (depending on
their spin). The spin-statistics theorem identifies the resulting quantum statistics that differentiates fermions from
bosons. According to this methodology: Particles normally associated with matter are fermions. They have half-
integer spin and are divided into twelve flavors. Particles associated with fundamental forces are bosons and they
have integer spin.

Common elementary particles
Several estimates imply that practically all the matter, when measured by mass, in the visible universe (not
including dark matter) is in the protons of hydrogen atoms, and that roughly 10 protons exist in the visible
                                                 80                                  [5]
universe (Eddington number), and roughly 10 atoms exist in the visible universe. Each proton is, in turn,
composed of 3 elementary particles: two up quarks and one down quark. Neutrons and other particles heavier
than protons, as well as helium and other atoms with more than one proton, are so rare that their total mass in
the visible universe is much less than the total mass of protons in hydrogen atoms. Lighter particles of matter,
although equal (electrons) or vastly more (neutrinos) numerous than protons, are so much lighter than protons,
that their total mass in the visible universe is again much less than the total mass of all protons.

Some estimates imply that practically all the matter, when measured by numbers of particles, in the visible
universe (not including dark matter) is in the form of neutrinos, and that roughly 10 elementary particles of
                                                        [6]                                      97
matter exist in the visible universe, mostly neutrinos. Some estimates imply that roughly 10 elementary
particles exist in the visible universe (not including dark matter), mostly photons, gravitons, and other massless
force carriers.

Discovery of Electrons: Cathode Rays

             DISCHARGE TUBE
   Discharge tube is a glass tube fitted with two electrodes placed opposite to each other. The tube is sealed and
   contains a vacuum pump. The function of vacuum pump is to reduced or change the pressure inside the
   tube. The two electrodes are connected to a high voltage battery.
                                                                                                               Page |5

       Different scientist tried different discharge tubes with different electrodes and different gases but results of all
       the experiment gave same value for charge to mass ratio. This shows that there is something common in all
       materials. It was concluded that all the substances in common.
       Experiment shows that these particles could be produces from any kind of material. Cathode rays consist of
       particles which are known as electrons.

    Atoms are electrically neutral. Hence after the discovery of the negatively charged constituent (electron) of an
    atom, attempts were made to discover the positively charged counterpart of electrons. By using a discharge tube
    containing a perforated cathode. Goldstein (1886) found that some rays passed through these holes in a direction
    opposite to that of the cathode rays.

                       Alt text: POSITIVE RAYS OR CANAL RAYS

    These are called the positive rays or canal rays. J.J. Thomson (1910) measured their charge by mass ratio from
    which he was able to deduce that these contain positive ions. Their properties are:

    They are positively charged.
    The positive charge is either equal to or whole number multiple of the charge on an electron.
   When hydrogen gas was filled in the discharge tube the positive charge on the positive rays was equal to the
    negative charge on an electron, and the mass was less than the hydrogen atom.
    Unlike cathode rays the properties of positive rays are characteristics of the gas in the tube.
    The deflection of positive rays under the influence of an electric or magnetic field is smaller than that of the
    cathode rays for the same strength of field. This shows that the positive rays have a greater mass than that of
    The mass of the positive rays depends on the atomic weights or molecular weights of the gases in the discharge
    tube. The charge/mass ratio also varies because the change in positive charge on the rays. It may be either
    equal to or integral multiple of the charge on an electron.
    The lightest of all particles identified in positive rays from different elements was one with a mass very slightly
    less than that of hydrogen atom (or nearly equal to H-atom). The lightest positively charged particle is called a
    proton (P or P ). Positive rays are atomic or molecular resides from which some electrons have been removed.
    The removed electrons constitute the cathode rays and the positive residues form the positive or canal rays.

    The Quantum Mechanical Model of the Atom
    Energy Is Quantized
                                                                                                              Page |6

After Max Planck determined that energy is released and absorbed by atoms in certain fixed amounts known
as quanta, Albert Einstein took his work a step further, determining that radiant energy is also quantized—he
called the discrete energy packets photons. Einstein‘s theory was that electromagnetic radiation (light, for
example) has characteristics of both a wave and a stream of particles.

The Bohr Model of the Atom
In 1913, Niels Bohr used what had recently been discovered about energy to propose his planetary model of the
atom. In the Bohr model, the neutrons and protons are contained in a small, dense nucleus, which the electrons
orbit in defined spherical orbits. He referred to these orbits as ―shells‖ or ―energy levels‖ and designated each by
an integer: 1, 2, 3, etc. An electron occupying the first energy level was thought to be closer to the nucleus and
have lower energy than one that was in a numerically higher energy level. Bohr theorized that energy in the form
of photons must be absorbed in order for an electron to move from a lower energy level to a higher one, and is
emitted when an electron travels from a higher energy level to a lower one. In the Bohr model, the lowest energy
state available for an electron is the ground state, and all higher-energy states are excited states.
Orbitals and Quantum Numbers
In the 1920s, Werner Heisenberg put forth his uncertainty principle, which states that, at any one time, it is
impossible to calculate both the momentum and the location of an electron in an atom; it is only possible to
calculate the probability of finding an electron within a given space. This meant that electrons, instead of traveling
in defined orbits or hard, spherical ―shells,‖ as Bohr proposed, travel in diffuse clouds around the

To describe the location of electrons, we use quantum numbers. Quantum numbers are basically used to
describe certain aspects of the locations of electrons. For example, the quantum numbers n, l, and ml describe
the position of the electron with respect to the nucleus, the shape of the orbital, and its special orientation, while
the quantum number msdescribes the direction of the electron‘s spin within a given orbital.
Below are the four quantum numbers, showing how they are depicted and what aspects of electrons they
                           Has positive values of 1, 2, 3, etc. As n increases, the orbital becomes larger—this
Principal quantum
                           means that the electron has a higher energy level and is less tightly bound to the
number (n)
                           Has values from 0 to n – 1. This defines the shape of the orbital, and the value of l is
Second quantum
                           designated by the letters s, p, d, and f, which correspond to values for l of 0, 1, 2, and 3.
number or azimuthal
                           In other words, if the value of l is 0, it is expressed as s; if l = 1 = p, l = 2 = d, and l = 3
quantum number (l )
                           = f.
Magnetic quantum           Determines the orientation of the orbital in space relative to the other orbitals in the
number (ml)                atom. This quantum number has values from -l through 0 to +l.
                           Specifies the value for the spin and is either +1/2 or -1/2. No more than two electrons
Spin quantum number
                           can occupy any one orbital. In order for two electrons to occupy the same orbital, they
                           must have opposite spins.
Orbitals that have the same principal quantum number, n, are part of the same electron shell. For example,
orbitals that have n = 2 are said to be in the second shell. When orbitals have the same n and l, they are in the
same subshell; so orbitals that have n = 2 and l = 3 are said to be 2f orbitals, in the 2f subshell.
Finally, you should keep in mind that according to the Pauli exclusion principle, no two electrons in an atom can
have the same set of four quantum numbers. This means no atomic orbital can contain more than two electrons,
and if the orbital does contain two electrons, they must be of opposite spin.

In case of light some phenomenon like diffraction and interference can be explained on the basis of its wave
character. However, the certain other phenomenon such as black body radiation and photoelectric effect can be
explained only on the basis of its particle nature. Thus, light is said to have a dual character. Such studies on light
were made by Einstein in 1905.
                                                                                                        Page |7

Louis de Broglie, in 1924 extended the idea of photons to material particles such as electron and he proposed
that matter also has a dual character-as wave and as particle.

Derivation of de-Broglie Equation:

The wavelength of the wave associated with any material particle was calculated by analogy with photon.

In case of photon, if it is assumed to have wave character, its energy is given by

E = hv                                 …(i)

(According to the Planck‘s quantum theory)

Where nth frequency of the wave and ‗h‘ is is Planck‘s constant

If the photon is supposed to have particle character, its energy is given by

E = mc                                 … (ii)

(according to Einstein‘s equation)

where ‗m‘ is the mass of photon, ‗c‘ is the velocity of light.

By equating (i) and (ii)
hv = mc
But v = c/λ

h c/λ = mc

(or) λ = h /mc

The above equation is applicable to material particle if the mass and velocity of photon is replaced by the mass
and velocity of material particle. Thus for any material particle like electron.

λ = h/mv or λ =      where mv = p is the momentum of the particle.

The Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with
half-integer spin) may occupy the same quantum state simultaneously. A more rigorous statement is that the total
wave function for two identical fermions is anti-symmetric with respect to exchange of the particles. The principle
was formulated by Austrian physicist Wolfgang Pauli in 1925.

For example, no two electrons in a single atom can have the same four quantum numbers; if n, l, and ml are the
same, ms must be different such that the electrons have opposite spins, and so on.

Integer spin particles, bosons, are not subject to the Pauli exclusion principle: any number of identical bosons can
occupy the same quantum state, as with, for instance, photons produced by a laser and Bose–Einstein

The Pauli exclusion principle governs the behavior of all fermions (particles with "half-integer spin"), while bosons
(particles with "integer spin") are not subject to it. Fermions include elementary particles such as quarks (the
constituent particles of protons and neutrons), electrons and neutrinos. In addition, protons and neutrons
(subatomic particles composed from three quarks) and some atoms are fermions, and are therefore subject to
the Pauli exclusion principle as well. Atoms can have different overall "spin", which determines whether they are
fermions or bosons — for example helium-3 has spin 1/2 and is therefore a fermion, in contrast to helium-4 which
has spin 0 and is a boson. As such, the Pauli exclusion principle underpins many properties of everyday matter,
from its large-scale stability, to the chemical behavior of atoms.

"Half-integer spin" means that the intrinsic angular momentum value of fermions is (reduced Planck's constant)
times a half-integer (1/2, 3/2, 5/2, etc.). In the theory of quantum mechanics fermions are described by
antisymmetric states. In contrast, particles with integer spin (called bosons) have symmetric wave functions;
                                                                                                                                Page |8

unlike fermions they may share the same quantum states. Bosons include the photon, the Cooper pairs which
are responsible for superconductivity, and the W and Z bosons. (Fermions take their name from the Fermi–Dirac
statistical distribution that they obey, and bosons from their Bose–Einstein distribution).

Radius and Energy Levels of Hydrogen Atom:

Consider an electron of mass ‗m‘ and charge ‗e‘ revolving around a nucleus of charge Ze (where, Z = atomic
number and e is the charge of the proton) with a tangential velocity v. r is the radius of the orbit in which electron
is revolving.

By Coulomb‘s Law, the electrostatic force of attraction between the moving electron and nucleus is Coulombic
           2 2
force = KZe /r

K = 1/4π∈o (where ∈o is permittivity of free space)

               9            2       –2
K = 9 x10 Nm C

                                                            2       –2
In C.G.S. Units, value of K = 1 dyne cm (esu)

The centrifugal force acting on the electron is mv /r

Since the electrostatic force balances the centrifugal force, for the stable electron orbit.

     2             2 2
mv /r= KZe /r                                               … (1)

         2                  2
or       v = KZe /mr                                             … (2)

According to Bohr‘s postulate of angular momentum quantization, we have

mvr = nh/2π

v = nh/2πmr

 2                      2       2 2
v = n2h2/4π m r                                                 … (3)

Equating (2) and (3)

                    2 2               2       2
KZe2/mr = n h /4π m2r

                                              2 2   2   2
Solving for r we getr = n h /4π mKZe

Where n = 1, 2, 3 - - - - - ∞

Hence only certain orbits whose radii are given by the above equation are available for the electron. The greater
the value of n, i.e., farther the energy level from the nucleus the greater is the radius.

The radius of the smallest orbit (n=1) for hydrogen atom (Z=1) is ro.

         2 2       2            2         2             -34 2                2   -31           -19 2    9             –11
ro = n h /4π me K = 1 x (6.626 x 10 ) / 4x(3.14) x9x10                                 x (1.6x10 ) x9x10 =5.29 x 10         m=0.529 Å

Radius of n orbit for an atom with atomic number Z is simply written as

rn = 0.529 x n /z Å

The atom is built up by filling electrons in various orbitals according to the following rules.
                                                                                                           Page |9

Aufbau Principle: This principle states that the electrons are added one by one to the various orbitals in order of
their increasing energy starting with the orbital of lowest energy. The increasing order of energy of various orbital
is 1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,6p,5f,6d,7p……………………

How to remember such a big sequence? To make it simple we are giving you the method to write the increasing
order of the orbitals. Starting from the top, the direction of the arrow gives the order of filling of orbitals.

Alternatively, the order of increasing energies of the various orbitals can be calculated on the basis of (n + l ) rule.

The energy of an orbital depends upon the sum of values of the principal quantum number (n) and the azimuthal
quantum number ( l ). This is called (n +l ) rule. According to this rule,

―In neutral isolated atom, the lower the value of (n + l ) for an orbital, lower is its energy. However, if the two
different types of orbitals have the same value of (n +l ), the orbitals with lower value of n has lower energy‘‘.

Illustration of (n +l ) Rule:

Type           of       Value of Values of
                                           Values of (n+l)       Relative energy
orbitals                n        l

     1s                      1                   0       1+0=1   Lowest energy

     2s                      2                   0       2+0=2   Higher energy than 1s orbital

     2p                      2                   1       2+1=3
                                                                 2p orbital (n=2) have lower energy than 3s
     3s                      3                   1       3+1=4   orbital (n=3)


Write the electronic configuration of nitrogen (atomic number = 7)



Write the electronic configuration of following:

     2-                              2+
(i) S ( Z = 16 ) (ii) Fe                  = ( Z = 26 )


     2     2        6    2       6
(i) 1s 2s 2p 3s 3p
                                                                                                     P a g e | 10

     2   2   6   2   6   6
(ii) 1s 2s 2p 3s 3p 3d

 Rutherford's gold foil experiment has proved that atom has a nucleus; but it did not provide any information
about the state of electrons in atoms! However theories like matter wave, dual nature of matter, uncertainty
principle, wave mechanics etc, are created based on the concept that electrons are in high-speed motion in
atoms. Today we believe that "Quantum behaviour" of electrons is responsible for all "strange properties"• of
electrons in atoms. But in reality, no experiment has ever proved that atomic electrons are in constant motion! In
fact, because of its inherent electric and magnetic field, it is absolutely impossible to move an electron around
the nucleus of an atom

  In a perfectly isolated atom, there are two types of forces acting on its electrons. They are attraction from the
nucleus and repulsion between electrons (in hydrogen atom attraction from the nucleus only). But these forces
cannot cause any kind of motion of electrons in atoms. In fact the widely accepted model of atom is not
consistent with the real facts. Since electrons are not constantly moving, there must be a force which prevents
the electrons from falling into the positive charged nucleus.
   Volume of atoms (for example, a hydrogen atom still possesses volume even after stripping off its electron) and
elastic nature of atoms (for example, gas atoms move randomly in high speed and bounce when they collide with
other atoms or its container) indicate that the nucleus of an atom is surrounded by a form of elastic matter. I
name this matter as "space matter". So there are three factors that determine the electron configuration in a
multi-electron atom. They are: a) attraction from the nucleus, b) repulsion between electrons and c) buoyant force
exerted by space matter. The electron configuration in a hydrogen atom is determined by two factors - Attraction
from the nucleus and buoyant force by space matter. Buoyant force is the only force which prevents the
innermost electrons of an atom from falling into the nucleus. The electrons other than one nearest to the nucleus,
repulsion with the electrons in the inner region as well as the buoyant force exerted by space matter keep the
electrons in an atom in its respective positions.
   Since an atom of an element creates its own characteristic pattern of spectrum lines when excited, and in cold
state the same atom creates absorption lines in the same frequencies that the atom creates its emission lines, we
can conclude that the electrons in an atom are situated in some kind of resonant columns.
   When a low-energy electron collides with a multi-electron atom, the atom emits long wavelength radiations. But
when a high-energy electron collides with the same atom, the atom can emit both shorter and longer wavelength
radiations. As a low-energy electron can only excite an atom's outer electrons, a high-energy electron is capable
of penetrating outer region of the atom and to excite inner electrons. So we can understand that, the space
matter density in the inner region of an atom is greater and it decreases with the increasing distance from the
nucleus and also, this difference in densities creates different resonant columns in an atom.


To top