Quantum physical sciences that arrangements with energy and power

Quantum Mechanics and Bonding Theories:


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A branch of physical sciences that arrangements with energy and power
and their impact on bodies.

Quantum Mechanics

branch of science which deals with matters behavior and its interactions with
the energy on atomic scale and it also explain very small things and subatomic



Quantum mechanics is the establishment of a few
related controls including nanotechnology, quantum science and synthesis of
physical science, auxiliary science, molecule physical science, and articles.

The term quantum mechanics was first used by Max
Born in 1924.

The acknowledgment by the general material science
group of quantum mechanics is because of its exact expectation of the physical
behavior of frameworks including frameworks where Newtonian mechanics falls

Indeed, even broad relativity is restricted in ways
quantum mechanics isn’t for portraying frameworks at the nuclear scale or
littler at low or high energies or at the most reduced temperatures.

During a time of experimentation and connected
science, quantum mechanical hypothesis has ended up being exceptionally
effective and reasonable.

The establishments of quantum mechanics date from
the mid-1800 yet the introduction of Quantum Mechanics date from proposed by
Max Planck in 1900.

Albert Einstein and Niels Bohr soon influenced
critical commitments to what to is currently called the old quantum theories.

Be that as it may, it was not until 1924 that a more
entire picture rose with Louis de Broglie’s issue wave theory and the genuine
significance of quantum mechanics turned out to be clear.

The obstruction that produces shaded groups on
bubbles cannot be clarified by a model that describe light as a molecule.

It can be clarified by a model that portrays it as a

The illustration indicates sine waves that look like
waves on the surface of water being reflected from two surfaces of a film of
differing width, however that portrayal of the wave idea of light is just a
rough relationship.

Early analysts varied in their clarifications of the
key idea of what we now call electromagnetic radiation.

Some kept up that light and different frequencies of
electromagnetic radiation are made out of particles, while others declared that
electromagnetic radiation is a wave.

In established physical science these thoughts are
commonly opposing.

As far back as the beginning of Quantum Mechanics
researchers have recognized that neither thought without anyone else can
clarify electromagnetic radiation.

Anyway, the achievement of quantum mechanics it has
some questionable module.

Quantum theory

Quantum theory is the hypothetical premise of
present day physical science that clarifies the nature and behavior of matter
and energy on the atomic and subatomic level. The nature and behavior of matter
and energy at that level is sometime referred to as quantum mechanics and
quantum physics.


In 1900 physicist Max Planck displayed his quantum
theory to the German Physical Society. Planck had tried to find the reason that
radiation from a shining body changes in shading from red to orange and finally
to blue as its temperature rises.

 He found that
by making the assumption that energy existed in singular units similarly that
matter does, as opposed to similarly as a constant electromagnetic wave as had
been earlier expected and was in this way quantifiable he could discover the
solution to his study. The presence of these units became the first assumption
of quantum theory.


Planck composed a mathematical equation including a
figure to represent to these individual units of energy which it called quanta.
The equation described the phenomenon very well. Planck found that at certain
discrete temperature levels energy from a glowing body will involve occupy
different areas of the spectrum.

Planck accepted there was a theory yet to rise up
out of the disclosure of quanta, yet actually their exceptionally presence
suggested a totally new and essential comprehension of the laws of nature.
Planck won the Nobel Prize in Physics for his hypothesis in 1918 very
advancements by different scientists over a thirty year time period all
contributed to the modern comprehension of quantum theory.

Main point of this theory

Energy is not emitted or absorbed continuously.
Energy is emitted or absorbed in a discontinuous manner and in the form of wave
packets. Each wave packet or quantum is associated with a definite amount of
energy .In case of light the quantum of energy is called photon.

The amount of energy associated with a
radiation is proportional to the frequency (V) of the radiation.



‘h’ is Plank’s constant and its value is .

A body can emit or absorbed energy only
in term of quantum.



The frequency ‘v’ is related to the
wavelength of the photon as





The energy of a photon is related to
frequency, wavelength and wave number. Greater the wave number of photons
greater is the energy associated with them. The relationship of energy, frequency,
wavelength, wave number about the photon of light are accepted by scientists
and used by Bohr in his atomic model.

Classical mechanics

                      The branch of mechanics
in which we study about the motion of the large objects . In classical
mechanics each particle has certain mass. Classical mechanics is based on the
newton law of motion

1.      An
object will stay at rest and moving with the constant velocity until an
unbalanced force act on that object.

2.      If
an unbalanced force act on body acceleration will produce in the body this
acceleration is directly proportional to the force and inversely proportional
to the mass of that body.


3.      Action
and reaction are equal but direction is opposite.s

theory of chemical bonding

 Many atoms can combine to form particular
molecules f0r example chlorine and sodium atoms form NaCl molecules.

 But atoms of the same type can also form bonds
as for example in the case of hydrogen.

the establishment of quantum theory the explanation of chemical bonding cannot
be understandable by chemists.

between ions as in the negatively charged chlorine ion and the positively charged
sodium ion, could, to be sure be understood in the light of the Coulomb
attraction between oppositely charged bodies it remained however unexplainable
that two similar atoms which are electrically neutral as for example two
hydrogen atoms could form a bound state homopolar bonding.

 Here it only became possible with the aid of
quantum mechanics to attain a fundamental understanding.  In the case of ionic bonding this is also
known as hetero polar bonding basic new understanding have been through developed
by quantum theory.

For example
it must be understood
why the ions form in the first place, and why the electron which is transferred
from sodium to chlorine thus finds an energetically more favorable state.

Quantum Numbers

Electron which are present in an
atom completely defined by its four quantum numbers .four types of quantum
numbers which are described the electron completely.

Principal Quantum Number

Azimuthal Quantum Number

Spin Quantum Number )

Magnetic Quantum Number  

Quantum Number

It is represented by n, the different energy
levels in Bohr’s atom represent by ‘n’ which is called principal quantum
number. It has values non zero, positive integers up to infinity.

n = 1, 2, 3, 4……..

The value of n represent the energy levels
in which the electrons revolves around the nucleus. There are notation K, L, M,
N which are used to donate the different shell. For example n=1 so it is K
shell for n=2 then it is L shell and so on, the position of electron in an atom
also determine by the value of n. If the electron at larger distance from the
nucleus the value of n greater will be the distance of electron from the

Azimuthal quantum number

This is used to represent the sub shell values of Azimuthal quantum
number are


The values of quantum number are depends
upon the n. Different shells are represented by these values which are denoted
by small latters s, p, d and f. They stand for sharp, principle, diffuse and
fundamentals respectively. The series of lines absorbs in the atomic spectrum
are define by these terms. Value of Azimuthal quantum number starts from zero.
Shape of sub shell depends upon the value of L. It may be dumbbell spherical or
complicated shape.

Magnetic quantum number:

In Bohr atomic model it has seen
that strong magnetic field split a spectral line further. For explaining this
splitting a third quantum number is used which is called magnetic quantum
number. Its values are


The value of  depends upon the value if




This represents that for a given value of the total
value of are {+1}

Spin Quantum Number

There is one electron in Alkali metals
outermost shell. The emission spectra can be record when the outermost electron
goes to a ground state from excited state. Spectra is observed by means of high
resolving power spectrometer it is found that in spectrum each line consist of
pair of lines it is doublet line structure.

Angular momentum of the electron are
described by Spin Quantum Number. Electron moves around towards axis have
angular momentum and orbital angular momentum. The angular momentum is a
vector. The spin quantum number have both direction and magnitude.

Chemical bond

                    A force of attraction
between the two atom or molecules which hold them togather is called chemical


Valence Bond Theory

This theory was
introduced by Heitler and London in 1927 which is based on the concept of
atomic orbitals, Electronic configuration of elements, the overlapping of
orbitals and Hybridization of orbitals.

The overlapping of
orbitals results in the formation chemical bond and the election are localized
in the bond region due to overlap.

 Valence bond theory also described the
electronic structure of molecules as it says that electron fills the atomic
orbitals of an atom with in a molecule and nucleus of one atom is attracted to
the electrons of another atom. Heitler and London proposed that the
electron wave of the valence orbital on one atom overlap the electron wave of
the other bonding orbitals to form a covalent bond .The required conditions for
this overlap of electron wave of orbitals are.

 The two
overlapping orbitals must have valance orbitals and must have half-filled and
also must retain their identities.

The valence half-filled orbitals of the atoms
should close to each other with axis of their orbitals in proper arrangements.

Let us consider an example of the
formation of H2 molecule.

A bond is formed by the head to head overlapping of the
atomic orbitals.

When there is the bond formation occur both of these
atoms come close to each other and interact with each other they are not
identifiable. There are two possibilities

H2B? case A

.H1B? case B

= ?A (1). ?B (2)

?2 =?A (2). ?B (1)

Here ? is a wave function.

True wave function is ?1+?2

                                           ? =
C1?1 + C2?2

C1 and C2 are the mixing

In case of  H2
molecule C1 = ±C2

It means that if C1 = 1 and C2
= ± 1

Therefore the two possibilities occur for the wave
function. One corresponding to the C1 = 1 and C2 = 1 and
the other is C1 = 1 and C2 = -1.

? = ?A (1).?B (2) + ?A (2).?B (1)

                      ? = ?A (1).?B (2)
_ ?A (2).?B (1)

Pauling has described that the calculation of Es
propose by Hitter and london can be enhance by considering that the additional
ionic character in which both the electrons are attached to the same atom. So
new equation will be;

                       ?3 = ?A (1).
?A (2)

                       ?4 = ?B (1).
?B (2)

By adding these four equations we will get final

? = ?A (1). ?B (2) +?A (2). ?B
(1) + ?A (1). ?A (2) +?B (1).?B (2)

? = ? covalent + ? ionic



v  The covalent bond is formed by the overlapping of
half-filled orbitals of two different atoms. Due to overlapping the electron
density between two bonded atoms increases and give stability to the molecule
first the carbon forms bonds to four hydrogen atoms and then second the bond
angles are much longer then the angel between two p orbitals.

v  So, for binding of such types and other different
molecules is accomplished by another process as hybridization

v  We cannot examine the procedure of obtaining hybrid
orbitals in mathematics so can give following assumption.

v  The number of standard atomic orbitals added
together always equal to number of hybrid orbitals formed .Total number is

v  The particular combination of standard atomic
orbitals added together determine the shapes and angles of hybrid orbital

v  The particular type of hybridization that occur is
the one that yield the lowest overall energy for the molecule.


Molecular Orbital Theory:

The molecular orbital approach review the entire molecule is
a single unit. It describe the atomic orbitals of the combining atom overlap
with each other to make new orbitals which are as molecular orbitals. The
molecular orbitals surround two or more nuclei of the bonded atom. After
overlapping two atomic orbitals forms two molecular orbitals which are differ
in energy. One of them has lower energy which is called as bonding orbital and
the other of high energy is called as anti-bonding molecular orbital. The
bonding Molecular orbital is symmetrical about the axis joining the nuclei of
the molecular axis. It is define as sigma  bonding molecular orbital while the other is
called as antibody molecular orbital.

The filling of electron in molecular
orbital is carried out by three different principles including as

Afbau’s principle

Hund’s rule

Pauli’s exclusion principle;

There are different examples describing
the scheme of molecular orbitals just like molecular orbital concept in
diatomic molecules as  and.

In  there is only one electron with in the valence
shell hence two hydrogen atoms combines and so in the formation of molecule
there are two electrons in bonding orbital and the anti-bonding orbital is
empty. Bond order is calculated by using formula as no of electrons in bonding
orbital subtracted by the no of electron in anti-bonding orbitals.

So far we have considered s and s orbital overlap for the
formation of molecular orbitals of hydrogen molecule. Other type of overlap
occurring between p and p atomic orbitals is to form new molecular orbitals.
There are three 2p atomic orbitals directed along the three perpendiculars x, y
and z coordinates. For the formation of molecular orbitals from p orbital there
are two cases which are

Head on approach

Sideway overlap

Head on overlap:

In this type of overlap molecule has both of its electro in same
orbitals as in  and . In this case head on
overlap of p orbitals occurs. They are symmetrical to the nuclear axis.

Sideway overlap:

In sideway overlapping of atomic orbitals two, atomic orbitals
are parallel to each other as in case of  and  sideway overlap of atomic orbitals occurs.

The bonding molecular orbitals  or  have zero electron density on the nuclear axis
called the nodal plane. The electron density is distributed above and below the
nodal plane. On the other hand anti bonding molecular  and  have the low electron density in the region of
inter nuclear. The  and  having the same energy these are called
degenerate atomic orbitals. The pi- molecular orbitals  and   are degenerate. The  and  molecular orbitals also degenerate. Overall
six molecular orbital are formed from two sets of 2p atomic orbitals. Three are
known as bonding and the other three are anti-bonding. The bond is formed as a
result of linear overlap is known as sigma bond while the other bond formed as
the result of sideways overlap is called a pi-bond.

There are three bonding molecular orbital. The p-orbitals
overlap can lead to the formation of at the most three bonds one sigma and two
pi bonds.

Let us consider the formation of simple homo-nuclear diatomic
molecule such as hydrogen molecule in which two similar atoms are joined by an
electron pair. Although the atoms are identical but they are separated by  and.

Each hydrogen atom has single electron in its valence shell. The
effective overlap of wave function will take place when

The orbital have identical energy

The orbital overlap to a specific extent

Orbital have same symmetry

Wave functions are given as


C is replaced with ?


There are two possible wave functions showing for bonding and
anti-bonding orbitals given as



MOT in Helium

The electronic configuration is . The 1s orbital
combine to form one bonding   and one anti bonding  orbitals. In He-atom each atom contributes two
electron which are present in its valence shell. The  two electrons 
enters in bonding molecular orbital and two enter in anti bonding
molecular orbitals. When we calculate its bond order it results zero given as


And so  molecule will not form.


Other MOT diagrams for  and  are given as,

Diagram for  is given as;


Bond Order

Bond Order is defined as the number of bond formed between
two atoms after the atomic orbitals overlap with each other and it is taken as
the half of the difference between the number of bonding electrons and the
number of anti-bonding electrons.

For example the number of bond formed between the two
hydrogen atoms in the hydrogen molecule can be calculated as:

Number of electrons in the bonding orbitals=2

Number of electrons in the ant bonding orbitals =0

Bond Order =2-0/2 =1

Molecular orbitals which are formed from valence orbital are
consider in calculations of bonding order.

Bond Energy

Energy is released when a bond is formed between two atoms
and when bond is broken energy in same amount is absorbed.

Bond energy is defined as the energy is the average amount
of energy required to break the bonds of a particular type in one mole of the

It can be measured by the heat involved in a chemical
reaction. It is also known as bond enthalpy and it is measure of enthalpy
change at 298K. The bond energy is given in KJ per mole.

Bond length:

Bond length is the distance between the nuclei of two atoms
formed a covalent bond is called bond length.










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