Topic
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SLO,s
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Atomic Structure
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2.1
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2.1.1
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Discharge Tube Experiment:
All
gases air are bad conductors of electricity at normal pressure. But on high
voltage and low pressure, they become good conductor. The conduction of
electricity was first studied by WILLIAM COOKS. The apparatus used for this
purpose is called “DISCHARGE TUBE”.
Construction:
Discharge tube
consists of a cylindrical glass tube closed at both ends and fitted with two
metallic electrodes. These electrodes are connected to the positive and
negative terminals of a battery.
The discharge tube
also posses a side tube which is connected to a vacuum pump in order to
remove the gas or air from it. The removal of air or gas reduced pressure
inside the tube.
Working:
When
a high voltage is applied to a discharge tube at normal pressure, no
phenomenon is observed. But when the vacuum pump is started and most of the
gas inside the discharge tube is pumped out and the pressure is reduced to 1 torr, the tube soon begins to emit
a soft glow. This gives an indication that the gas in the tube begins to
conduct electricity. As the pressure is further reduced, the glowing rays
move towards anode. Since these rays are produced at the surface of the
cathode therefore these are called “CATHODE
RAYS”.
At still lower
pressure about 0.01 torr, the flow
from within the tube fades out and dark spaces appears in the discharge tube.
At this stage the glass tube at the anode end begins to emit a greenish
fluorescence.
Properties of Cathode Rays:
The various experiments
performed by different scientists indicate that the cathode rays possess the
following characteristics:
1. These rays travel in a straight
lines perpendicular to the cathode surface.
2. These rays produce sharp shadows
if an opaque object is placed in their path.
3. These rays emerge from cathode and
can be focused by using a concave cathode.
4. These rays can penetrate small
thickness of meter e.g. Aluminum or Gold foils
without producing any
perforation in it.
5. These rays can exert mechanical
pressure, showing they possess Kinetic Energy.
6. These rays are deflected in a
magnetic field. This behavior indicates
that they consist
of charged particles.
7. These rays are deflected towards
positively charge plate in an electrical field,
indicating that they consist
of negatively charged particles called ELECTRONS.
8. The charge to mass ratio (e/m) of
these rays is 1.76 x 1011 coulomb / Kg.
9. The charge and mass of these rays
are 1.6 x 10-19 coulomb & 9.1 x 10-31 Kg
respectively.
10. The rays were seen neither to depend
on the material of which the electrodes were
made nor upon the gas which is
filled in the tube.
Conclusion:
On
the basis of these properties, it was concluded that cathode rays are
negatively charged particles called “ELECTRONS”.
Since nature of the cathode rays does not change with the nature of the gas
and the cathode used in the tube, hence it can be safely that electrons are
the fundamental particles of all atoms.
DISCOVERY OF PROTON:
During
the study of the passage of electricity through gases at low pressure, it was
observed by Goldstein that, in
addition to cathode rays there are also other rays traveling in opposite
direction to the cathode rays, and if the cathode is perforated, then these
rays can pass through the perforations (canals) and accumulate at the behind
of cathode. He named these rays as “Positive
Rays” or “Canal Rays”.
Properties of Positive Rays:
1.These rays travel
in a straight line.
2.These rays are
deflected by electric and magnetic fields opposite to the cathode rays.
Therefore these are positively charged
rays.
3.These
rays are not emitted from anode but are produced from the ionization of gas as a
result of bombardment of electrons.
4.Their
positive charge was found to be equal to that of electron or simple multiple of it.
5.These
particles were found to be much heavier than electrons. The mass of these
particles were found to depend on the
kind of gas taken in the
discharge tube but it is
never less than that of an atom or hydrogen.
6.
Positive rays unlike cathode rays have different value of e/m depending
on the gas
present in the discharge tube.
Conclusion:
The
charge to mass ratio (e/m) of
these rays depends upon the natural of the gas in the discharge tube. The
highest (e/m) ratio is obtained in
case of hydrogen gas. Therefore hydrogen without electron (H+) is
the smallest positive particles of matter. This particle was given the name “PROTON” by Goldstein in 1986. Later on
Discovery of Neutron:
The
total mass of the protons and electrons in each atom are not sufficient to
account for the atomic masses of the different elements. For this reason,
scientists believed that there must be another heavy particle inside the
atom.
In 1932, James Chadwick discovered the third
particle in the nucleus of atom by means of artificial radioactivity.
Chadwick bombarded
the nucleus of Beryllium atoms with a particles and found that
it gave highly penetrating radiation. Chadwick put forward the suggestion
that these penetrating radiation were due to material particles with mass
comparable with that of an atom of hydrogen but carrying no charge. These
particles are called “Neutrons” The
neutrons must have come out from atoms on disintegration of the bombarded
element. This is indicated by the equation.
 4Be9
+ 2He4 6 C12 + 0n1 |
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2.2
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2.2.1
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Bohr’s Atomic Theory:
The weakness in the
Rutherford’s model and the formation of line spectrum were improved by Neil
Bohr, who proposed a new theory to explain the electronic structure of the
atom in 1913. This theory is based upon the following assumptions.
Assumptions:
1. Electrons
in an atom revolve around the nucleus in fixed circular which he called
orbits or energy levels.
2. As
long as an electron revolves in a particular energy level it does not emit or
absorb energy.
3. When
an electron absorbs energy, it moves to a higher energy level, further away
from the nucleus. When it loss energy, it returns
to a lower energy level, closer to the nucleus and the energy is emitted as light.
4. The
electron loses a definite quantity of energy called “Quantum”, when it jumps from an orbit of higher energy level to
lower energy level.
5. The
energy is emitted in the form of radiations. The frequency of the energy
emitted is directly proportional to the difference in energy between two levels.
i.e. E2 – E1 a u
E2
– E1 = hu
D E
= hu
where, E1 = Energy of electron in 1st
orbit.
E2
= Energy of electron in 2nd orbit.
DE =
Energy difference b/w two levels.
u = Frequency of the energy emitted.
h = Plank’s Constant
6. The
angular momentum (mvr) of an
electron in any orbit is integral
multiple of
 .
where,
m = mass of electron
v =
velocity of electron
r =
Radius of the orbit
n =
Quantum number
=
1, 2, 3, ……………
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2.2
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2.2.2
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Radius
of an Orbit:
Suppose an atom of Hydrogen with
atomic number ‘Z’ and electro with mass ‘m’ , charge ‘e’ is revolving around
its nucleus at the distance ‘r’.
The electrostatic force (centripetal force)
between the nucleus and the electron would be
The centrifugal force which keeps the electron
away from the nucleus would be
 . Since the electron is in equilibrium.
\
centrifugal force = centripetal force
\
 --------------
(i)
According to postulate of Bohr’s Theory:
 
Þ
 --------------
(ii)
Put this value of ‘v2’ in equation (i)
we have
Þ
Þ
Þ
Þ
Þ
 --------------
(iii) |
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2.2
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2.2.3
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Plank’s
Quantum Theory:
German physicist, Max Plank proposed this theory in 1900 to describe the origin of
the radiations from heated bodies. This theory is stated as:
“Radiant energy is emitted or absorbed by a body
in the form of small packets, called QUANTA,
instead of being continuously. This QUATA of energy are often called PHOTON.
Also the amount of energy given off or absorbed
is directly related to the frequency of the light emitted”.
i.e.
E a
u
=> E = hu
where E =
energy of quanta
u =
frequency of radiation
h
= Plank’s constant
= 6.625 x 10-34 J.sec
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2.2
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2.2.4
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Energy
of Electron:
An electron possess Kinetic
Energy due to its motion around the nucleus and the potential energy due to
the coulombic attraction force of the nucleus.
According to equation
Þ
Þ
Þ
 --------------
(iv)
Now P.E. =
Fcoul X Distance
Þ
Þ
The total energy of electro will be the sum of
its K.E. & P.E.
\
E = K.E + P.E
Þ
Þ
 --------------
(v)
We know that
\
Þ
Þ
 --------------
(vi)
Frequency:
Suppose and electron with energy
E2, jumps from higher energy state n2, to a lower
energy state n1, with energy E1. Then the energy
released DE
by the electron will be
DE
= E2 – E1
The energies E2 and E1 of
the electron will be
and
\
Þ 2
Þ
 -------------- (vii)
According to Bohr’s Postulate,
DE
= hu
Þ
Þ
 --------------
(viii)
Wave
Number:
The number of waves per unit
distance is called “Wave Number” , if “C” is the velocity of light then the
wave number is given by
Putting this value in eq. (viii) we have
Þ
Þ
 --------------
(ix)
But
 is a constant term which is called Rydberg constant
denoted by RH and has value 109678 cm-1.
Þ
 --------------
(x)
The expression is for wave number.
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2.5.1
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Heisenberg’s
Uncertainty Principle:
Statement:
According to this principle,
“The position & the momentum of an electron
cannot be determined accurately simultaneously. One is measured more
accurately, the other becomes equally more uncertain at any given instant.”
Mathematical
Expression:
If DPx is the
uncertainty in the determination of the momentum of a particle & Dx
was the uncertainly in the simultaneous determination of it’s position , then
the product of these two uncertainties is given by:
DPx
. Dx @ h
Thus if one of the two i.e. Px or X
was known exactly , then the uncertainty in its other would become infinite .
It means that the certainty of determination of one property introduces
uncertainty
For the determination of other.
Explanation:
The uncertainty arise due to the
fact that a light with shorter wave length than the located its position. But
the momentum of photon (particle of light) increases with decreasing its
wave-length.
An electron is so small a particle, that it will
be disturbed from its position, on colliding with a high momentum photon
particle used to locate it, & hence it is
not possible to say as to what actual position of electron is,
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2.5.2
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Orbit:
“The fixed circular path on
electron around the nucleus called “Shell”
or “Energy
Level” or “Orbit”.
These orbit are designated as K, L, M, N, etc.
The maximum number of electron in one orbit is “2n2“, where “n” is
the number of orbit. These orbit possess a definite amount of energy
increasing outwards from the nucleus.
Orbitals:
If a atomic spectrum is
observed, the spectral lines are found to be consist of two or more fine lines
closely packed together. Thus the electron In the same orbit may differ in
energy by small amount. Thus energy level are further divided into Sub – Energy Levels or “Orbitals”
& can be defined as
“Orbitals
are the regions
around the nucleus in which the
probability of finding the electron is maximum.”
The Orbitals have been named as s, p, d, f, etc.
The maximum no. of electron in s, p, d, f, are 2, 6, 10 & 14
respectively. Each orbit has “Orbital”
equal to its quantum number ‘n’. Thus the first orbit contain 1, the
second orbit has 2 (i.e. s & p) , the third orbit has 3 (i.e. s, p &
d) & fourth has 4 (i.e. s, p, d & f ) Orbitals.
SHAPES OF
ORBITAL
S –
orbital:
 All’s
Orbitals are spherical in shape with the nucleus at the centre. Therefore in
an ‘S’ orbital, the probability of
finding the electron is uniformly distributed around the nucleus. It has only one
possible orientation in space, because it
spread over all the three axes uniformly . It has no nodal plane.
P –
orbital:
The P - orbital are dumb-bell shaped
and they are oriented in the space
along the three mutually perpendicular
axis (x,y,z) and are called Px, Py
and Pz
orbitals. All the three P- orbitals are
perpendicular to each other.
These are degenerated orbitals, that are equal
energy. Each P – orbital has two lopes, one of which is labeled (+) and the
other is labeled (-).
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2.5.3
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Quantum
NumberS:
In 1926 Schrödinger was a mathematician who calculate the probability of
location of the electrons in an orbital. Quantum Numbers are the constant
used in Schrödinger. Wave equation
to describe the energy of an electron, the shape of orbitals an orientation
in space around the nucleus of atom. The four quantum numbers are:
ü
Principle quantum number
ü
Azimuthal quantum number
ü
Magnetic quantum number
ü
Spin quantum number
Principle
Quantum NumberS:
Principle quantum number
describes the size of an orbit and is represent by ‘n’. They have any
integral value i.e. n=1,2,3,………………… it never zero. The size and the energy of
orbital increase with increase the value of ‘n’.
Azimuthal
Quantum NumberS:
Azimuthal quantum number
describes the shape of an orbital and its represented by ‘l’. It can have integral values
ranging from zero to n-1 i.e. l=0,1,2,…………… (n-1)
If l =
o, the orbital is called s orbital
If l =
1, the orbital is called p orbital
If l =
2, the orbital is called d orbital
Magnetic
Quantum Numbers:
The magnetic quantum number
describes the different orientation of an orbital in the space in applied
magnetic field and it is represented by ‘m’. The value of m =- l to + l through zero. i.e. , m = -
l ….0….. + l.
If l =
2
Then m = -2 , -1, 0 , +1, +2
i.e. d-orbital has the five orientations.
Spin
Quantum Numbers:
It describes the direction of
spin of an electron around the nucleus of an atom and is represented by ‘s’.
Its values are = + ½ and – ½.
+ ½ spin for clockwise direction
- ½ spin for anti clockwise direction
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2.6.1
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2.7.1
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Principle
of Electronic Configuration:
The distribution of electron in
the orbitals of the atom is called electronic configuration. Following rules
are used in the filing of the electrons in any orbital.
(i)
Pauli exclusion principle
(ii)
Aufbau principle
(iii)
(n+ l)
rule
(iv)
Hund’s rule
Pauli
Exclusion Principle:
According to this principle “No
two electron of the same atom will have the same value of all its four
quantum numbers”.
Therefore in an atom two electrons may have a
maximum of three same quantum numbers, same value but the fourth would be
different. Thus in an orbital, when the value of n, l and m are same , the two electrons can occupy the same orbital
only there spin are opposite.
e.g. for 1st K shell
n=1,
l=0, m=0, s=+ ½
n=1,
l=0, m=0, s=- ½
Aufbau principle:
According to this rule the
electron are fed in various orbitals in order of increase orbital energy
starting with the one ‘s’ orbital”.
Hence electronic configuration of an atom can be
built up by placing the electrons to the lowest available orbital until the
total number of electrons added is equal to the atomic number ‘Z’. The
sequence of increasing orbital energy is below
1s, 2s,2p,3s,3p,4s,3d,4p,……………
(n+ l) Rule:
According to this rule “In
builting up the electronic configuration the orbitals with the lowest value
of (n+l)fills first, but when the
two orbitals have the same value of (n+ l),
the orbital with the lower value of ‘n’ fills first”.
Here ‘n’ and ‘l’
stands for principal and azimuthal quantum numbers respectively. Actually
this rule is used to determine the energy of any orbital and then we can
apply the Aufbau Principle. e.g. 3d – orbital is filled later than 4s –
orbital
\ 3d – orbital has (n+l ) = 3+2 = 5
4s
– orbital has (n+l ) = 4+0 = 4
Similarly 4p – orbitals fills before 5s – orbital
because 4p orbital has lesser value of ‘n’.
\ 4p– orbital has (n+l ) =
4+1 = 5
5s
– orbital has (n+l ) = 5+0 = 5
Hund’s
Rule:
According to this rule “When the
orbitals of same energy levels are available, then electrons are distributed
in orbitals in such a way as to give the maximum numbers of unpaired
electrons . Only when the orbital are separately occupied then the pairing of
electrons commences”.
This rule explain the filling of electrons in
degenerate (having same energy) orbitals like p,d,f. In simple, it state that
the electrons remain unpaired as far as possible. i.e. If there are available
orbitals of equal energy to the electrons, the electrons would lie in
separate orbitals and have same spin rather than to lie in the same orbital
and have paired spin.
  e.g. (N(Z=7) = 1s2, 2s2,2Px
, 2Py , 2Pz
is true
and not
1s2, 2s2,2Px, 2Py, 2Pz
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2.7.2
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RADIUS
OF THE FIRST ORBIT OF HYDROGEN ATOM:
R = n2 h2÷ 4л2
kmZe2
Where
h=6.63x10-34
J.s
k=9.00x109
J.m./C2
m=9.109x10-31kg
e=1.6x10-19C
л=3.14
Z=1
=(1)2(6.63x10-34)2÷4(22/7)2(9.00x109)(9.109x10-31kg)(1.6x10-19)2
=
0.529 x10-10 m
ENERGY OF AN ELECTRON IN THE FIRST ORBIT OF
HYDROGEN:
E=
(-) k e2 ÷ 2r
Where
r =0.529
x10-10 m
k=9.00x109
J.m./C2
e=1.6x10-19C
E= (-)
(9.00x109 J.m./C2)(1.6x10-19C) ÷ 2(0.529
x10-10 m)
= -2.178 x10-18J
"At still lower pressure about 0.01 torr, the flow from within the tube fades out and dark spaces appears in the discharge tube. At this stage the glass tube at the anode end begins to emit a greenish fluorescence."
ReplyDeleteSir I can not understand what is meant by this paragraph.