Structure of the atom manik

PHARM 1101
Md. Imran Nur Manik
Lecturer
Department of Pharmacy
Northern University Bangladesh

Structure of the Atom
Prepared By: Md. Imran Nur Manik; B.Pharm; M.Pharm Page 1
manikrupharmacy@gmail.com; Lecturer; Department of Pharmacy; Northern University Bangladesh.
Atom
The existence of atoms has been proposed since the time of early Indian and Greek
philosophers (400 B.C.) who were of the view that atoms are the fundamental building blocks of
matter.
According to them, the continued subdivisions of matter would ultimately yield atoms which
would not be further divisible. The word „atom‟ has been derived from the Greek word „a-tomio‟
which means „uncut able‟ or „non-divisible‟.
These earlier ideas were mere speculations and there was no way to test them experimentally.
These ideas remained dormant for a very long time and were revived again by scientists in the
nineteenth century.
Theories of Atomic Structure
The atomic theory of matter was first proposed on a firm scientific basis by John Dalton, a
British school teacher in 1803. His theory, called Dalton‟s atomic theory, regarded the atom as
the ultimate particle of matter.
The physical and chemical properties of elements and their compounds are essentially with the
structure of atoms. A systemic knowledge of the structure of atoms is, therefore, necessary for
the study of modern inorganic chemistry.
In this unit, we shall start with the experimental observations made by scientists towards the end
of nineteenth and beginning of twentieth century. These established that atoms can further be
divided into subatomic particles i.e. electrons, protons and neutrons.
Fundamental Particles of Atom
An atom is the smallest particles of an element having its own chemical identity and properties.
Atom consists of still smaller particles, such as electron, proton, neutron etc. into which it can
be subdivided. These particles are regarded as fundamental particles, because these are the
main constituents of atoms.
Classification of Fundamental Particles:
i) Permanent Fundamental Particles: The particles which play an important role for the formation of
structure of an atom and are present in all atoms (except hydrogen where neutron is absent) are called
permanent fundamental particles. There are three kinds of permanent fundamental particles such as
electron, proton and neutron.
Electron bears negative charge and revolves around the nucleus in a circular path. The mass of
electron is very small.
Proton bears the positive charge and stays at the nucleus with neutrons.
Neutron has no charge, i.e. it is neutral. It is placed in the nucleus with proton.
ii) Temporary Fundamental Particles:
The particles which exist in some atoms for short time are called temporary fundamental
particles. There are about 100 numbers of temporary fundamental particles in different atom
like positron, neutrino, antineutrino, meson etc.
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Discovery of Electron
Production of Cathode Rays:
In mid 1850s many scientists mainly Faraday began to study electrical discharge in partially
evacuated tubes, known as cathode ray discharge tubes. It is depicted in the following Fig.
Fig. Production of cathode rays in a discharge tube.
The knowledge about the electron was derived as a result of the electric discharge in a discharge tube.
The discharge tube consists of a glass tube with metal electrodes fused in the walls. The pressure inside
the tube can be reduced with a pump.
When the electrodes are connected to a source of high voltage (10,000 volts), an electric discharge
from high potential source is passed through a gas at pressure of 0.001 mm of Hg in the discharge
tube and the glass wall opposite to the cathode begins to glow with a very faint greenish light (or bluish
light depending on the composition of the glass of which the tube is made.)
This glow or fluorescence is formed due to the bombardment on the glass by certain rays which are
emitted from the cathode surface and move towards the anode with tremendous velocity. These rays
were called cathode rays by Goldstein since these were originated from the cathode.
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The results of this experiment are summarized below.
(i) The cathode rays start from cathode and move towards the anode.
(ii) These rays themselves are not visible but their behavior can be observed with the help of certain kind
of materials (fluorescent or phorosphescent) which glow when they are hit by the cathode rays.
(iii) In the absence of electrical or magnetic field, these rays travel in straight lines (Fig. 2.2)
Fig. Measurement of e/m for electrons.
(iv) In the presence of electrical or magnetic field, the behaviors of cathode rays are similar to that
expected from negatively charged particles, suggesting that the cathode rays consist of negatively
charged particles, called electrons.
(v) The characteristics of cathode rays (electrons) do not depend upon the material of electrodes and the
nature of the gas present in the cathode ray tube.
Thus, we can conclude that electrons are basic constituent of all the atoms.
The rays which proceed from the cathode and move away from it right angles in straight lines are called
cathode rays. They are deflected in electric and magnetic fields indicating that these rays carry electric
charge.
Properties of Cathode Rays
They travel in straight lines away from the cathode. e.g. Shadow of aluminium crosses.
They produce fluorescence (a glow) when they strike the glass wall of discharge tube.
They produce X-rays when they strike a metallic target.
Consist of moving particles with definite mass and velocity i.e. Momentum.
They can ionize gases.
They can pass through thin metal foil.
The cathode rays are deflected towards the positive pole of the electric field which proves that
the rays are associated with negative charges. The particles making up the cathode rays were all
identical and ultimately given the name electron by the Dutch Physicist H. A. Lorentz.
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(a) In 1897 J.J. Thomson showed that when cathode rays are passed through an electric field (i.e. when the
rays are passed between two electrically charged plates), they are deflected towards the positively charged
plate [Fig. 1.2 (a)], showing thereby that the particles constituting the cathode rays are negatively charged.
These negatively charged particles were called electrons by Thomson.
Fig. 1.2 (a) Cathode rays-are deflected in an electric field, showing- that the particles (i.e. electrons) constituting
the cathode rays are negatively charged.
(b)In 1895 J. Perrin showed that if a magnetic field is applied on cathode rays from top to bottom,
perpendicular to the plane of the paper as shown in Fig. 1.2 (b), cathode rays are deflected upwards in the
plane of the paper. This experiment also shows that the particles constituting the cathode rays are negatively
charged.
Fig. 1.2 (b) Cathode rays are deflected in a magnetic field, showing that the particles (i.e., electrons) constituting
the cathode rays are negatively charged.
Fig. 1.2. Experiment to show that the particles (i.e. electrons) constituting the cathode rays are negatively
charged.
Definition of an Electron
Having known the charge and mass of an electron, it can be defined as:
An electron is a subatomic particle which bears charge –1.6010–19 coulomb and has mass
9.110–28 g.
Alternatively, an electron may be defined as:
A particle which bears one unit negative charge and mass 1/1835th of a hydrogen atom.
Since an electron has the smallest charge known, it was designated as unit charge by Thomson.
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Discovery of Proton
In 1886, German physicist , Eugen Goldstein used a discharge tube provided with a cathode
perforated with extremely fine holes and observed that when the electrodes are connected to a
source of high voltage (10,000 volts), not only cathode rays of electrons were originated from
the cathode moving from cathode towards anode but also new type of colored rays were
simultaneously originated from the anode moving from anode towards cathode through the fine
holes or canals in the cathode causing a glow on the wall opposite to anode.
Initially these rays were called canal rays, since they pass through the canals or holes of the
cathode. These are also called anode rays as they seem to originate from the anode.
Sir J. J. Thomson has shown that these rays consist of particles carrying a positive charge and
hence he named them positive rays.
Fig. Production of positive (anode) rays
Explanation of the Production of Positive Rays
When a high voltage is applied across the metallic electrodes of a discharge tube filled with a gas
under reduced pressure, the molecules of the gas are dissociated into atoms.
Now when high speed electrons (i.e. cathode rays) originated from cathode strikes these atoms,
the atoms are converted into cations which pass through the holes of the cathode and constitute
positive rays.
The electrons obtained in the conversion of the gaseous atoms into cations move towards anode
as negative rays.
M + e
-
→ M
+
+ 2e
-
Gaseous
atoms
Originated from
cathode
Pass through the
perforated cathode
as positive rays
Move towards
anode as negative
rays
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Fig. Explanation of the production of positive rays (Illustration).
The characteristics of these positively charged rays are listed below.
(i) Unlike cathode rays, the positively charged particles depend upon the nature of gas present in
the cathode ray tube. These are simply the positively charged gaseous ions.
(ii) Some of the positively charged particles carry a multiple of the fundamental unit of electrical
charge.
(iii) The behavior of these particles in the magnetic or electrical field is opposite to that observed for
electron or cathode rays.
The smallest and lightest positive ion was obtained from hydrogen and was called proton.
This positively charged particle was characterized in 1919.
Thomson Model of Atom
J. J. Thomson, in 1898, proposed that an atom possesses
a spherical shape (radius approximately 10–10 m) in which the
positive charge is uniformly distributed. The electrons are
embedded into it in such a manner as to give the most stable
electrostatic arrangement (Figure). Many different names were
given to this model, for example, plum pudding, raisin pudding or
watermelon.
This atomic model was given up after some time,
since it could not explain the large deflection suffered by α—
particles in Rutherford‟s experiment.
Discovery of Neutron
Up to 1932, it was postulated that an atom is composed
of only proton and electron.
Mass of an atom is due to proton as mass of electron is negligible.
Rutherford noticed that mass of different atoms cannot be explained if it is supposed that atom
is composed of proton and electron. He predicted, in 1920, that some kind of neutral particles
having mass equal to proton must be present in an atom.
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These particles were discovered by James Chadwick (1932) by bombarding a thin sheet of
beryllium by α-particles when electrically neutral particles having a mass slightly greater than that
of the protons were emitted. He named these particles as neutrons.
Experiment
A stream of alpha-particles was directed from a polonium source to a Beryllium target.
A charge detector was placed behind the Beryllium target.
A new radiation was produced which no charge on them had indicated by charge detector.
The reaction in Chadwick‟s experiment converted a „Be‟ atom into a Carbon atom through the
nuclear reaction.
Summary of Electron, Proton & Neutron
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Rutherford‟s α—particle scattering experiment
Rutherford and his students (Hans Geiger and Ernest Marsden) bombarded very thin gold foil with
α—particles. Rutherford‟s famous α—particle scattering experiment is represented in the following Fig.
A stream of high energy α—particles from a radioactive source was directed at a thin foil
(thickness ∼ 100 nm) of gold metal. The thin gold foil had a circular fluorescent zinc sulphide screen
around it. Whenever α—particles struck the screen, a tiny flash of light was produced at that point.
Rutherford‟s observation
Fig. Rutherford and Marsden's -particle scattering experiment.
It was observed that:
(i) Most of the α-particles passed through the gold foil undeflected.
(ii) A small fraction of the α-particles was deflected by small angles.
(iii) A very few α-particles (∼1 in 20,000) bounced back, that is, were deflected by nearly 180°.
Fig. How nuclear atom causes scattering of -particles.
On the basis of the observations, Rutherford drew the following conclusions regarding the structure of
atom:
(i) Most of the space in the atom is empty as most of the α-particles passed through the foil
undeflected.
(ii) A few positively charged α-particles were deflected. The deflection must be due to enormous
repulsive force showing that the positive charge of the atom is not spread throughout the atom
as Thomson had presumed. The positive charge has to be concentrated in a very small volume
that repelled and deflected the positively charged α-particles.
(iii) Calculations by Rutherford showed that the volume occupied by the centre is negligibly small as
compared to the total volume of the atom. The radius of the atom is about 10-10 m, while that
of centre is 10-15 m. One can appreciate this difference in size by realizing that if a cricket ball
represents the centre, then the radius of atom would be about 5 km.
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Rutherford‟s Nuclear Model of Atom
On the basis of above observations and
conclusions, Rutherford proposed the nuclear
model of atom .
According to this model:
(i) The positive charge and most of the mass
of the atom was densely concentrated in
extremely small region. This very small
portion of the atom was called nucleus by
Rutherford.
(ii) As the atom is electrically neutral, so the equal number of electrons as that of protons surround
the nucleus.
(iii) The nucleus is surrounded by electrons that move around the nucleus with a very high speed in
circular paths called orbits. Thus, Rutherford‟s model of atom resembles the solar system in
which the nucleus plays the role of sun and the electrons that of revolving planets.
(iv) Electron and the positive nucleus are held together by electrostatic forces of attraction. This
attraction force is counter-balanced by the outward force of electron.
Drawbacks of Rutherford Model
Rutherford‟s nuclear model of an atom is like a small scale solar system with the nucleus playing
the role of the massive sun and the electrons being similar to the lighter planets. When classical
mechanics is applied to the solar system, it shows that the planets describe well-defined orbits
around the sun. The theory can also calculate precisely the planetary orbits and these are in
agreement with the experimental measurements. The similarity between the solar system and
nuclear model suggests that electrons should move around the nucleus in well-defined orbits.
According to the electromagnetic theory of Maxwell, charged particles when move around
another charged particle, then they should emit electromagnetic radiation. Therefore, an
electron in an orbit will emit radiation; the energy carried out by radiation comes from electronic
motion. The orbit will, thus, continue to shrink. But this does not happen. Hence, the
Rutherford model cannot explain the stability of an atom.
Another serious drawback of the Rutherford model is that it says nothing about the electronic
structure of atoms i.e. how the electrons are distributed around the nucleus and what are the
energies of these electrons.
It could not explain how the spectral lines are produced by the simplest atoms like hydrogen
atoms when an electron jumps from one orbit to another.
Wavelength: The wavelength is defined as the distance between two
successive crests or troughs of a wave.
Wavelength is denoted by the Greek letter (lambda).
Frequency: The frequency is the number of waves which pass a given
point in one second.
Frequency is denoted by the letter (nu) and is expressed in hertz (hz).
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Spectrum
A spectrum is an array of waves or particles which is spread out according to the increasing or
decreasing of some properties such as wavelength or frequency.
Types of Spectra
Depending on the nature of the source emitting the radiation there are two types of spectra.
(1) Emission spectra
-Emission spectra are further of two types:
(a) Continuous spectrum
(b) Discontinuous spectrum which may be -
- Band spectrum
or, - Line spectrum (atomic spectrum)
(2) Absorption spectra
1. Emission Spectra
Emission spectra can be obtained from the substances which emit light on excitation. Their excitation
can be done as follows:
1. By heating the liquid or solid substances in a flame at high temperature. These substances
become incandescent at high temperature i.e. when these substances are heated at high
temperature they emit light. Electric light, lime light, arc light are the examples of such solid
substances.
2. By passing an electric discharge through a gas at low pressure.
3. By passing electric current through thin filament of a high melting point metal like tungsten.
Emission spectra are of the following two types:
a. Continuous Spectrum
When a narrow beam of sunlight or any white light is
allowed to pass through a prism and then allowed to fall on
a screen, it gets resolved into seven colours i.e. violet,
indigo, blue, green, yellow, orange and red (VIBGYOR). This
phenomenon is called dispersion and the band of seven
colours observed on the screen is called visible spectrum.
In this spectrum, since one
colour merges into another
without any break or
discontinuity (i.e. one colour
changes gradually into
another), the spectrum thus
obtained is called continuous
spectrum. This series of
bands that form a continuous
rainbow of colours, is called a
Continuous Spectrum.
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The Wave Nature of Light
Refraction is the bending of light when it passes from one medium to another of different
density.
 Speed of light changes.
 Light bends at an angle depending on its wavelength.
 Light separates into its component colors.
b. Discontinuous spectrum
Discontinuous spectrum may be band or line spectrum.
Band spectrum:
The band spectrum consists of a number of bright bands separated by dark spaces. Each
band is sharp at one end and fades gradually in the other end. Band spectrum is the property of
molecules and generally given by the compounds or gases like nitrogen and oxygen molecules at low
temperature and pressure. Since this spectrum is characteristics of molecules it is also called molecular
spectrum.
Line spectrum:
When an atom of an element absorbs energy, it gets excited. The excited atom emits
light radiations of a characteristic colour. When this emitted radiation is allowed to pass through a
prism, it is resolved into several individual lines. The pattern of different lines of the radiation is called
line spectrum. It is also called atomic spectrum because this spectrum is given by the atoms of an
element.
- - Helium was first discovered in the sun in 1868 with the help of its spectrum.
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2. Absorption spectra
If, in the arrangement to get a continuous spectrum of white light, a substance is placed
between the white light source and the prism, we get an absorption spectrum. This spectrum appears in
the form of dark lines in a particular region of the continuous spectrum of white light. For example, if a
solution of NaCl is placed between the white light source and prism, the continuous spectrum of white
light is found to be crossed by two dark lines in the yellow region of the spectrum. If the white light
source is removed, the whole of the continuous spectrum disappears leaving behind only two bright
yellow light. These two dark lines produced by NaCl solution in the continuous spectrum of white light
are known as absorption line spectrum.
Hydrogen Spectrum (Origin of spectral line)
When an electric discharge is passed through gaseous hydrogen in a discharge tube, the
H2 molecules dissociate and the energetically excited hydrogen atoms produced emit
electromagnetic radiation of discrete frequencies.
The hydrogen spectrum consists of several series of lines named after their discoverers. Balmer
showed in 1885 on the basis of experimental observations that if spectral lines are expressed in
terms of wavenumber ( ν ), then the visible lines of the hydrogen spectrum obey the following
formula :
Where, n is an integer equal to or greater than 3 (i.e., n = 3,4,5,….)
The series of lines described by this formula are called the Balmer series. The Balmer series of
lines are the only lines in the hydrogen spectrum which appear in the visible region of the
electromagnetic spectrum.
Lyman found a series of
lines in the ultraviolet
region of hydrogen
spectrum. Later, three
more scientists Paschen,
Bracket and Pfund found
three more series of lines
in the infrared region of
hydrogen spectrum which
were named after them.
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The Swedish spectroscopist, Johannes Rydberg, noted that all series of lines in the hydrogen spectrum
could be described by the following expression :
Where, n1 = 1,2……..
n2 = n1 + 1
The value 109,677 cm-1 is called the Rydberg constant for hydrogen and the value of n1 is fixed for a
particular series of lines.
The five series of lines that correspond to n1 = 1, 2, 3, 4, 5 are known as Lyman, Balmer, Paschen,
Bracket and Pfund series, respectively. Table 2.3 shows these series of transitions in the hydrogen
spectrum.
The five series of lines that correspond to n1 = 1, 2, 3, 4, 5 are known as Lyman, Balmer, Paschen,
Bracket and Pfund series, respectively. Table 2.3 shows these series of transitions in the hydrogen
spectrum.
Fig : shows the Lyman, Balmer and Paschen series of transitions for hydrogen atom.
Fig. Hydrogen spectral series on a Bohr atom energy diagram.
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Of all the elements, hydrogen atom has the simplest line spectrum. Line spectrum becomes more and
more complex for heavier atom. There are, however, certain features which are common to all line
spectra
1. Line spectrum of an element is unique.
2. There is a regularity in the line spectrum of each element i.e. the radiations emitted from an
atom have a fixed frequency and wavelength in the spectrum.
Problem
3. What are the frequency and wavelength of a radiation emitted during a transition from n = 5
state to the n = 2 state in the hydrogen atom?
Bohr‟s Atomic Model
Neils Bohr (1913) was the first to explain quantitatively the general features of hydrogen atom structure
and its spectrum. Bohr‟s model for hydrogen atom is based on the following postulates:
i) The electron in the hydrogen atom can move around the nucleus in a circular path of fixed
radius and energy. These paths are called orbits, stationary states or allowed energy states.
These orbits are arranged concentrically around the nucleus.
ii) The energy of an electron in the orbit does not change with time. However, the electron will
move from a lower stationary state to a higher stationary state when required amount of energy
is absorbed by the electron or energy is emitted when electron moves from higher stationary
state to lower stationary state.
iii) The frequency of radiation absorbed or emitted when transition occurs between two stationary
states that differ in energy by ΔE, is given by :
ΔE = (E2 – E1) = hν —————————————(1)
Where, E1 and E2 are the energies of the lower and higher allowed energy states respectively.
This expression is commonly known as Bohr‟s frequency rule.
iv) The angular momentum of an electron in a given stationary state can be expressed as in
equation-
mevr = n.h/2π ——————————————(2)
v) Thus, an electron can move only in those orbits for which its angular momentum is integral
multiple of h/2π. That is why, only certain fixed orbits are allowed.
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Reasons for the Failure of the Bohr Model
1. Bohr model can explain only hydrogen atom spectrum but it can‟t explain the spectrum of atoms
having several electrons.
2. An electron is regarded as a charged particle moving in well-defined circular orbits around the
nucleus. But modern research reveals that electrons may revolve in elliptical orbits also.
3. Further, an orbit is a clearly defined path and this path can be completely defined only if both the
position and the velocity of the electron are known exactly at the same time. This is not possible
according to the Heisenberg‟s uncertainty principle. (Its position and momentum cannot be precisely
pinned down)
4. For the transformation of electrons from one energy level to another only one line should be
obtained in the spectrum. But after analyzing the spectrum, several fine lines are obtained. Bohr‟s atom
model can‟t explain these features.
Orbit & Orbital
 Orbit and orbital are not synonymous.
 Orbit: An orbit, as proposed by Bohr, is a circular path around the nucleus in which an electron
moves.
 Orbital: It is a region of space around the nucleus where the probability of finding an electron is
maximum.
Differences between Orbit and Orbital (home work)
Quantum Numbers
A large number of orbitals are possible in an atom. Qualitatively these orbitals can be distinguished by
their size, shape and orientation. An orbital of smaller size means there is more chance of finding the
electron near the nucleus. Atomic orbitals are precisely distinguished by what are known as quantum
numbers. Each orbital is designated by three quantum numbers labeled as n, l and m.
Thus, the numbers which express the size, shapes, direction of the orbital from the nucleus and the
spins of the electron on their own axis are called quantum numbers.
There are four types of quantum numbers.
1. Principal quantum number
2. Subsidiary quantum number or Azimuthal quantum number
3. Magnetic quantum number
4. Spin quantum number
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1. Principle Quantum Number:
This number expresses the orbits or principal energy
levels in which the electron revolves round the
nucleus. This is also referred to as major energy
level. It is denoted by n ( n =1, 2, 3 etc). The value
of „n‟ represents the shells or energy levels.
For the first shell, n =1, for the second shell, n = 2
and so on. Thus, with the increase in the value of
„n‟, the number of allowed orbit increases. All the
orbitals of a given value of „n‟ constitute a single
shell of atom and are represented by the following
letters
 n = 1 2 3 4 …………
 Shell = K L M N …………
Principal quantum number represents any particular orbit. The value of n gives roughly the
binding force and the distance between the nucleus and the electron and also the energy it
possesses. The first energy level is the one nearest the nucleus.
Consequently, it is strongly bound with nucleus and possesses the lowest energy.
Size of a shell increases with increase of principal quantum number „n‟.
In other words, the electron will be located away from the nucleus.
Maximum possible number of electrons in a shell is 2n2.
2. Azimuthal or Subsidiary Quantum Number:
The main energy levels (or shells) of electron may be considered as being made up of one or more
sub-levels (sub-shells). The quantum number which represents the existence of an electron in a sub-shell
is called the subsidiary or Azimuthal quantum number. It is designated by the letter „l‟.
It defines the three dimensional shape of the sub-shell. For a given value of n, l can have values
ranging from 0 to (n – 1),
that is, for a given value of n, the possible value of l are: l = 0, 1, 2, ………. (n-1)
For example, when n = 1, value of l is only 0.
 For n = 2, the possible value of l are 0 and 1.
 For n = 3, the possible values of l are 0, 1 and 2.
The number of sub-shells in a principal shell is equal to the value of n.
For example in the first shell (n = 1), there is only one sub-shell which corresponds to l = 0.
For (n = 2), there are two sub-shells (l = 0, 1) in the second shell; for (n = 3) three (l = 0, 1, 2) in
third shell and so on.
Sub-shells corresponding to different values of l are represented by the following symbols.
 Value for l: 0 1 2 3 …………
 Notation for sub-shell: s p d f …………
Maximum number of electrons in a sub-shell is 2(2l+1). Where, l = 0,1,2,3…..etc.
Example: If n = 7, what are the possible values of l?
The following table shows the permissible values of „l‟ for a given principal quantum number and the
corresponding sub-shell notation.
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n l Sub-shell notation
1 0 1s
2 0 2s
2 1 2p
3 0 3s
3 1 3p
3 2 3d
4 0 4s
4 1 4p
4 2 4d
4 3 4f
3. Magnetic Quantum Number:
The magnetic quantum number was introduced to explain the orientation of orbitals in space
particularly under the influence of an applied magnetic field. This is designated by „m‟.
The magnetic quantum number „m‟ determines the number of orbitals and their orientation
within a subshell. The permitted values of m are dependent upon l.
For any sub-shell (defined by „l‟ value), 2l+1 values of m are possible and they are from –l to +l
including 0.
Thus, for l = 0, the only permitted value of m = 0, [2(0)+1 = 1, one s orbital].
For l = 1, m can be -1, 0 and +1 [2(1)+1 = 3, i.e. -2, -1, 0, 1, or 2. three p orbitals; the value of
2l+1 will be three and there will be three different orbitals. ].
For l = 2, m = -2, -1, 0, +1 and +2, [2(2)+1 = 5, five d orbitals].
Each orbital in an atom, therefore, is defined by a set of values for n, l and m. An orbital
described by the quantum numbers n = 2, l = 1, m = 0 is an orbital in the p sub-shell of the
second shell.
The following chart gives the relation between the sub-shell and the number of orbitals associated with
it.
Values of l 0 1 2 3 4 5
Sub-Shell Notation s p d f g h
Number of orbitals 1 3 5 7 9 11
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4. Spin Quantum Number:
The three quantum numbers are used to define its size/energy, shape and orientation. But all
these quantum numbers are not enough to explain the line spectra observed in the case of
multi-electron atoms, that is, some of the lines actually occur in doublets (two lines closely
spaced), triplets (three lines, closely spaced) etc. This suggests the presence of a few more
energy levels than predicted by the three quantum numbers.
In 1925, George Uhlenbeck and Samuel Goudsmit proposed the presence of the fourth
quantum number known as the spin quantum number (ms).
In other words, an electron has, besides charge and
mass, intrinsic spin angular momentum. Spin angular
momentum of the electron, a vector quantity, can
have two orientations relative to the chosen axis.
These two orientations are distinguished by the spin
quantum numbers ms which can take the values of +
or -. These are called the two spin states of the
electron and are normally represented by two arrows,
↑ (spin up) and ↓ (spin down).
Two electrons that have different ms values (one +1/2 and the other -1/2) are said to have opposite
spins.
An orbital cannot hold more than two electrons and these two electrons should have opposite spins.
Summary of Quantum Numbers
To sum up, the four quantum numbers provide the following information :
1) „n‟ defines the shell, determines the size of the orbital and also to a large extent the energy of
the orbital. There are n subshells in the nth shell.
2) „l‟ identifies the subshell and determines the shape of the orbital. There are (2l+1) orbitals of
each type in a subshell, that is, one s orbital (l = 0), three p orbitals (l = 1) and five d orbitals
(l = 2) per subshell. To some extent l also determines the energy of the orbital in a multi-electron
atom.
3) „m‟ designates the orientation of the orbital. For a given value of l, m has (2l+1) values, the
same as the number of orbitals per subshell. It means that the number of orbitals is equal to the
number of ways in which they are oriented.
4) ms refers to orientation of the spin of the electron.
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Principal Quantum
number (n)
Subsidiary
Quantum number (l)
L=0 to n-1
Sub-
levels
Magnetic
Quantum number (m)
M=+l to –l including 0
Orbital
number
1(K) 0 1s 0 1
2(L)
0
1
2s
2p
0
+1, 0, -1
1
3
3(M)
0
1
2
3s
3p
3d
0
+1, 0, -1
+2, +1,0,-1,-2
1
3
5
4(N)
0
1
2
3
4s
4p
4d
4f
0
+1, 0, -1
+2, +1,0,-1,-2
+3, +2, +1,0,-1,-2,-3
1
3
5
7
Distribution of Electrons in Atoms:
The electrons are arranged among the known elements in seven main energy levels designated
by the principal quantum numbers n=1, 2, 3, 4, 5, 6 and 7. These principal levels are divided
into sub-levels indicated by s, p, d, and f.
The first energy level (n=1) which has only one sub-level is designated as 1s. The second energy
level (n=2) has two sub-levels designated as 2s and 2p, the third (n=3) energy level has three
sub-levels designated as 3s, 3p and 3d and the fourth energy level n=4 has four sub-levels 4s,
4p, 4d and 4f.
The sub-levels are further divisible into orbitals. An s sub-level is made up of one orbital; a p
sub-level - three orbitals; a d sub-level-five orbitals and f sub-level - seven orbitals.
Each electron orbital can accommodate a maximum of two electrons of opposed spins.
Thus, one s orbital can hold a maximum of two electrons. The three p orbitals can hold a
maximum of 6 electrons etc.
Electronic Configuration of Atom
According to quantum mechanics, the arrangement of electrons of an atom in different orbitals is called
the electronic configuration. This electronic configuration follows some rules i.e.
1) Pauli‟s Exclusion Principle
2) Aufbau‟s law
3) Hund‟s rule of maximum multiplicity
Pauli‟s Exclusion Principle
The number of electrons to be filled in various orbitals is restricted by the exclusion principle
given by the Austrian scientist Wolfgang Pauli.
Pauli‟s exclusion principle states that, „no two electrons in an atom can have the same set of
values for all four quantum numbers.‟
This principle can also be stated as-“only two electrons may exist in the same orbital and they
must have opposite spin.”
It means that the two electrons of the same atom can have the same values for three of their
quantum numbers, but the fourth quantum number must be different for the two electrons.
Thus, two electrons may have orbits of the same size, shape and orientation in space provided
they have opposed spins.
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For example, helium has two electrons. According to Pauli‟s exclusion principle, the values of the
quantum numbers for these two electrons will be as follows-
For electron 1, e1: n = 1; l = 0; m = 0; s = +1/2
For electron 2, e2: n =1; l = 0; m = 0; s = -1/2
Aufbau‟s Law
Aufbau is a German word which means build up or construction. It is for this reason that the principle is
also often called building up principle or construction principle. This principle states as follows
The orbitals are filled up with electrons in the increasing order of their energy.
The principle can also be restated as, „During electronic
configuration, electrons first go to the orbital of low energy and then
systematically to the orbital of higher energy.‟ This happens because
the orbital with lower energy is more stable.
The energy of various orbitals of an atom a multi-electron atom
increases as
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s ......
The energy of an orbital is determined by the sum of principal
quantum number (n) and the azimuthal quantum number (l).
This rule is called (n + l) rule. There are two parts of this rule:
(a) The orbitals with the lower value of (n + l) have lower energy than the orbitals of higher (n + l) value.
And hence is filled up first with electrons.
(b) When two or more orbitals have the same value of (n + 1), the orbital with lower value of n is lower
in energy and hence is filled up first with electrons.
Example: Considering 4s and 3d orbital:
For the 4s orbital, the value of, n=4 and the value of l=0 (s). The total value of (n+l)= 4+0= 4
Again, for the 3d orbital, the value of, n=3 and the value of l=2 (d). The total value of (n+l)= 3+2= 5
So, electrons will go to 4s orbital first between 4s and 3d orbital.
On the other hand, If the two orbital have the same value of (n+l) then electrons will go to that orbital
first which has lower principal quantum number.
Considering 3d and 4p orbital:
For the 3d orbital, the value of n=3 and the value of l=2 (d). The total value of (n+l) = 3+2=5
For the 4p orbital, the value of n=4 and the value of l=1(p). The total value of (n+l) = 4+1=5
Hence, electrons will go to the 3d orbital first.
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Hund‟s Rule of Maximum Multiplicity
This rule is applied to the electronic configuration in the orbitals of same energy. The distribution of
electron in a set of degenerate orbitals like px, py, pz set; dxy, dyz, dzx, dz
2, dx
2, dy
2 set etc. of a given
sub-shell takes place in such a way to give the maximum number of unpaired electrons and these
electrons must have the same direction of spins.
This rule can also be stated as- „The orbital of a given sub-shell is first filled singly and then the pairing
of electrons in each orbital begins.‟
Illustration of the principle:
In order to illustrate the principle, let us consider the electronic configuration of oxygen atom
whose atomic number is eight. According to this principle the degenerated 2px, 2py and 2pz orbitals will
be first filled singly with electrons numbered as 5, 6 and 7. These 3 electrons will have the same spin.
Electron number 8 which is the last electron will pair with the electron number 5 in 2px orbital.
Fig. Electronic configuration of oxygen atom (atomic number = 8). The boxes represent orbitals, The arrows
indicate the electrons while the numbers shown below the arrows represent the electron number.
Stable configuration:
It‟s been observed that half-filled or fully filled orbitals with same energy have more stable
configuration. That‟s why np3, np6, nd5, nd10, nf7 or nf14 orbitals are more stable.
For this reason, d5s1 configuration occurs rather than d4s2 and d10s1 occurs rather than d9s2.
Example,
Cr(24)=1s2 2s2 2p6 3s2 3p6 4s2 3d4 (Aufbau‟s law)
=1s2 2s2 2p6 3s2 3p6 4s1 3d5 (Stable configuration)
Here, the latter one occurs in case of Chromium to acquire more stable configuration.
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