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 STRUCTURE OF ATOM,sharma sir,scceducation,chemistry ,9718041826,free notes,free cbse study material,ncert solution,
The rich diversity of chemical behaviour of different elements is due to the differences in the internal structure of atoms of these elements. The existence of atoms has been proposed since the time of early Indian and Greek philosophers (400 B.C.)
Atoms are the fundamental building blocks of matter’.

The word ‘atom’ has been derived from the Greek word ‘a-tomio’ which means ‘uncutable’ or ‘non-divisible’. (These earlier ideas were mere speculations.)
The atomic theory of matter was first proposed on a firm scientific basis by John Dalton, a British school teacher in 1808. His theory, called Dalton’s atomic theory, regarded the atom as the ultimate particle of matter .
In this unit we study about the experimental observations made by scientists towards the end of nineteenth and beginning of twentieth century. These established that atoms can be further divided into subatomic particles, i.e., electrons, protons and neutrons

The major problems before the scientists at that time were:
a) to account for the stability of atom after the discovery of sub-atomic particles,
b) to compare the behaviour of one element from other in terms of both physical and chemical properties,
c) to explain the formation of different kinds of molecules by the combination of different atoms
d) to understand the origin and nature of the characteristics of electromagnetic radiation absorbed or emitted by atoms.
Dalton’s atomic theory was able to explain
1. The law of conservation of mass, 
2. The law of constant composition and 
 3.The law of multiple proportion
However, it failed to explain the results of many experiments,
e.g. The substances like glass or ebonite when rubbed with silk or fur generate electricity.

Discovery of Electron
In 1830, Michael Faraday showed that if electricity is passed through a solution of an electrolyte, chemical reactions occurred at the electrodes, which resulted in the liberation and deposition of matter at the electrodes. He formulated certain laws. These results suggested the particulate nature of electricity.
We know “Like charges repel each other and unlike charges attract each other”.
In mid 1850s many scientists mainly Faraday began to study electrical discharge in partially evacuated tubes, known as cathode ray discharge tubes

 cathode ray tube is made of glass containing two thin pieces of metal, called electrodes, sealed in it. The electrical discharge through the gases could be observed only at very low pressures and at very high voltages
The pressure of different gases could be adjusted by evacuation. When sufficiently high voltage is applied across the electrodes, current starts flowing through a stream of particles moving in the tube from the negative electrode (cathode) to the positive electrode (anode).

These were called cathode rays or cathode ray particles
The flow of current from cathode to anode was further checked by making a hole in the anode and coating the tube behind anode with phosphorescent material zinc sulphide. When these rays, after passing through anode, strike the zinc sulphide coating, a bright spot on the coating is developed(same thing happens in a television set)  A cathode ray discharge tube with perforated anode
The results of these experiments are summarised below.

(i) The cathode rays start from cathode and move towards the anode.

(ii) These rays themselves are not visible but their behaviour can be observed with the help of certain kind of materials (fluorescent or phosphorescent) which glow when hit by them.

Note—Television picture tubes are cathode ray tubes and television pictures result due to fluorescence on the television screen coated with certain fluorescent or phosphorescent materials.

(iii) In the absence of electrical or magnetic field, these rays travel in straight lines. (As they cast shadow if we place an opaque object in their path.)

(iv) In the presence of electrical field, they move towards +ve electrode, 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.
Charge to Mass Ratio of Electron ( e/m ratio )

In 1897, British physicist J.J. Thomson measured the ratio of electrical charge (e) to the mass of electron (me ) by using cathode ray tube and applying electrical and magnetic field perpendicular to each other as well as to the path of electrons.
Thomson concluded that the amount of deviation of the particles from their path in the presence of electrical or magnetic field depends upon.

(i).The magnitude of the negative charge on the particle, greater the magnitude of the charge on the particle, greater is the interaction with the electric or magnetic field and thus greater is the deflection.

(ii) the mass of the particle — lighter the particle, greater the deflection.

(iii) the strength of the electrical or magnetic field — the deflection of electrons from its original path increases with the increase in the voltage across the electrodes, or the strength of the magnetic field.
When only electric field is applied, the electrons deviate from their path and hit the cathode ray tube at point A. Similarly when only magnetic field is applied, electron strikes the cathode ray tube at point C. By carefully balancing the electrical and magnetic field strength, it is possible to bring back the electron to the path followed as in the absence of electric or magnetic field and they hit the screen at point B. By carrying out accurate measurements on the amount of deflections observed by the electrons on the electric field strength or magnetic field strength, Thomson was able to determine the value of e/me as:
Where me is the mass of the electron in kg and e is the magnitude of the charge on the electron in coulomb (C). Since electrons are negatively charged, the charge on electron is –e.
Charge on the Electron
R.A. Millikan (1868-1953) devised a method known as oil drop experiment (1906-14), to determine the charge on the electron. Charge on the electron to be – 1.6 × 10–19C. The present accepted value of electrical charge is – 1.6022 × 10–19 C. The mass of the electron (me) was determined by combining these results with Thomson’s value of e/meratio.

Discovery of Protons and Neutrons
Electrical discharge carried out in the modified cathode ray tube led to the discovery of particles carrying positive charge, also known as canal rays. The characteristics of these positively charged particles are as--

(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) The charge to mass ratio of the particles is found to depend on the gas from which these originate.

(iii) Some of the positively charged particles carry a multiple of the fundamental unit of electrical charge.

(iv) In electric field they move towards –ve electrode it means they have positive charge.

(v) The smallest and lightest positive ion was obtained from hydrogen and was called proton. After discovery of two oppositely charged particles scientist thought, how these particles present in a very small atom without disturbing to each other.
First atomic model given by Sir J.J.Thomson.
Thomson Model of Atom

J. J. Thomson, in 1898, proposed that an atom possesses a spherical shape (radius approximately 10–10m) 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  Many different names are given to this model, for example, plum pudding, raisin pudding or watermelon. This model can be visualised as a pudding or watermelon of positive charge with plums or seeds (electrons) embedded into it.
Although this model was able to explain the overall neutrality of the atom.

Thomson was awarded Nobel Prize for physics in 1906, for his theoretical and experimental investigations on the conduction of electricity by gases.

Drawbacks of this model—
1. It could not explain the stability of atom.
2. it could not give the theoretical explanations of a no. of experiments.

Rutherford’s First Nuclear Model of Atom
Rutherford’s experiment (Rutherford’s alpha particle scattering experiment)-- Rutherford and his students (Hans Geiger and Ernest Marsden) bombarded very thin gold foil with ά–particles.
Rutherford’s famous alpha–particle scattering experiment
Observation--(i) most of the ά – particles passed through the gold foil undeflected.
(ii) a small fraction of the ά particles was deflected by small angles.
(iii) a very few ά – particles (~1 in 20,000) bounced back, that is, were deflected by nearly 180°.
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 –particles passed through the foil un deflected.

(ii) A few positively charged – 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 ά – particles.

(iii) Calculations by Rutherford showed that the volume occupied by the nucleus 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 nucleus is 10–15m.

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) 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. So this model also named as ‘Planetary model’.
(iii) Electrons and the nucleus are held together by electrostatic forces of attraction.

Discovery of neutron---
According to the calculations of Rutherford w.r.t. the mass of atom, later, a need was felt for the presence of electrically neutral particle as one of the constituent of atom. These particles were discovered by Chadwick (1932) by bombarding a thin sheet of beryllium by -particles.
4Be9 + 2He4(ά )----6C12+ 0n1
An electrically neutral particles having a mass slightly greater than that of the protons was emitted. He named these particles as neutrons.
Table --- Properties of Fundamental Particles

Millikan’s oil drop experiment—
This method used to determine the electric charge on microscopic particles.
X-Rays---(In the later half of the nineteenth century different kinds of rays were discovered)
Wilhalm Röentgen (1845-1923) in 1895 showed that when electrons strike a material in the cathode ray tubes, produce rays which can cause fluorescence in the fluorescent materials placed outside the cathode ray tubes. Since Röentgen did not know the nature of the radiation, he named them X-rays (means- Extra).
It was noticed that X-rays are produced effectively when electrons strike the dense metal anode, called targets.

Properties of x-rays—1. These are not deflected by the electric and magnetic fields.
2. They have a very high penetrating power through the matter and that is the reason that these rays are used to study the interior of the objects i.e. fractured bones, cracks in pipe lines e.t.c.
3. These rays are of very short wavelengths (~0.1 nm) and possess electro-magnetic character.

Radioactivity—Henri Becqueral (1852-1908) observed that there are certain elements which emit radiation on their own and named this phenomenon as radioactivity and the elements known as radioactive elements.

This field was developed by Marie Curie, Piere Curie, Rutherford and Fredrick Soddy. It was observed that three kinds of rays i.e. , β- and γ-rays are emitted. Rutherford found that ά-rays consists of high energy particles carrying two units of positive charge and four unit of atomic mass. He concluded that ά- particles are helium nuclei as when ά- particles combined with two electrons yielded helium gas. β-rays are negatively charged particles
similar to electrons. The γ-rays are high energy radiations like X-rays, are neutral
in nature and do not consist of particles. As regards penetrating power, -particles
<β - rays (100 times that of –particles) <-rays
(1000 times of that -particles).

Atomic Number and Mass Number
The number of protons present in the nucleus is equal to atomic number (Z ) e.g. ----
In order to keep the electrical neutrality, the number of electrons in an atom is equal to the number of protons (atomic number, Z ).
Atomic number (Z) = number of protons in the nucleus of an atom = number of electrons in a neutral atom While the positive charge of the nucleus is due to protons.
The mass of the nucleus, due to protons and neutrons. The protons and neutrons present in the nucleus are collectively known as nucleons.
The total number of nucleons is termed as mass number (A) of the atom.
mass number (A) = number of protons (Z) + number of neutrons (n)
Presentation of an atom-- (At no.) ZX A(At.mass no.)

Isobars and Isotopes
Isobars are the atoms with same mass number but different atomic number for example, 6C14 and 7N14.
Atoms with identical atomic number but different atomic mass number are known as Isotopes.The difference between the isotopes is due to the presence of different number of neutrons present in the nucleus. For example, Isotopes of hydrogen atom, 99.985% of hydrogen atoms contain only one proton, called as protium( 1H1), second is deuterium 1 proton and 1 neutron (1D2, 0.015%) and third is tritium 1 proton and 2 neutrons (1T3). Other examples of isotopes are: carbon atoms containing 6, 7 and 8 neutrons besides 6 protons ( 6C12, 6C13, 6C14); chlorine atoms containing 18 and 20 neutrons besides 17 protons (17Cl35, 17Cl 37).

Note-- Isotopes show same chemical behaviour as chemical properties of atoms are controlled by the number of electrons, equal to number of protons in the nucleus. Number of neutrons present in the nucleus have very little effect on the chemical properties of an element.
Isobars show different chemical properties as they different no. of electrons.

Drawbacks of Rutherford Model
Rutherford compared his nuclear model of an atom with solar system i.e. nucleus is like sun
the iveplaying the role of the
onsproperties.and the electrons are similar to the planets, So electrons move around the nucleus in well defined orbits. (From, the coulomb force = k q1q2/r2 where q1 and q2 are the charges, r is the distance of separation of the charges and k is the proportionality constant and it is is mathematically similar to the gravitational force between electron and the nucleus = G m1m2/r2. where m1 and m2 are the masses, r is the distance of separation of the masses and G is the gravitational constant.)
However, when a body is moving in an orbit even with constant speed, it undergoes acceleration because of changing direction. So an electron in the Rutherford nuclear model is under acceleration.
According to the electromagnetic theory of Maxwell, charged particles when accelerated
should emit electromagnetic radiation (This feature does not exist for planets since they are uncharged). Therefore, an electron in an orbit will emit radiation, the energy carried by radiation comes from electronic motion. The orbit will thus continue to shrink.
(Calculations show that it should take an electron only 10–8 s to spiral into the nucleus.)
But this does not happen.

1. Thus, the Rutherford model cannot explain the stability of an atom.

Note--If we asume electrons are stationary around the nucleus. If the electrons were stationary, electrostatic attraction between the dense nucleus and the electrons would pull the electrons toward the nucleus to form a mini Thomson’s model of atom.
2. Rutherford model says nothing about the electronic structure of atoms and energies of the electrons.

Results observed from the studies of interactions of radiations with matter have provided certain information regarding the structure of atoms and molecules. Neil's Bohr utilised these results to improve Rutherford model.
Two important theories used by Bohr to gave his model. These were:

(i) Dual character of the electromagnetic radiation which means that radiations possess both wave like and particle like properties, and

(ii) Experimental results regarding atomic spectra which can be explained only by assuming quarantined (definite) electronic energy levels in atoms.

Wave Nature of Electromagnetic Radiation
James Maxwell (1870) suggested that when electrically charged particle moves under acceleration, alternating electrical and magnetic fields are produced and transmitted. These fields are transmitted in the forms of waves called electromagnetic Waves/ radiation.
Note--Light is the form of radiation. In earlier days (Newton) light was supposed to be made of particles (corpuscles). In the 19th century, wave nature of light was established.
Maxwell t the first toy to gave his model fined orbits.suggested bihisuggested light waves are associated with oscillating electric and magnetic character.
 The electric and magnetic field components of an electromagnetic wave.
These components have the same wavelength, frequency, speed and amplitude, but they vibrate in two mutually perpendicular planes

Few simple properties of electromagnetic wave motion.
(i) The oscillating electric and magnetic fields produced by oscillating charged particles are perpendicular to each other and both are perpendicular to the direction of propagation of the wave.

(ii) Unlike sound waves or water waves (matter waves), electromagnetic waves do not require medium and can move in vacuum.

(iii) There are many types of electromagnetic radiations, which differ from one another in wavelength (or frequency). These constitute electromagnetic spectrum (Fig.). Different regions of the spectrum are identified by different names.

(iv) Different kinds of units are used to represent electromagnetic radiation.
These radiations are characterised by frequency and wavelength .

Frequency (ν)It is defined as the number of waves that pass a given point in one second. The SI unit for frequency (ν) is hertz (Hz, s–1), after Heinrich Hertz.

Wavelength λ-have the units of length. It is the length of one wave i.e. one trough and one crust.
Note--In vacuum all types of electromagnetic radiations, regardless of wavelength, travel -----s the length of one wave i.e. one trough and one the same speed, i.e., 3.0 × 108 m s–1---(2.997925 × 108 m s–1, to be precise). This is called speed of light and symbol is ‘c‘. The frequency (ν), wavelength (λ) and velocity of light (c) are related as--
The other commonly used quantity specially in spectroscopy,

Wave numberIt is defined as the number of wavelengths per unit length. Its units are reciprocal of wave length unit, i.e., m–1, cm–1 (not SI unit).
Fig. (a) The spectrum of electromagnetic radiation. (b) Visible spectrum. The visible region is only a small part of the entire spectrum .

Particle Nature of Electromagnetic Radiation : Planck’s Quantum Theory
Experimental phenomenon diffraction* and interference** explained the wave nature of the
electromagnetic radiation.
(Note * Diffraction is the bending of wave around an obstacle.
** Interference is the combination of two waves of the same or different frequencies to give a wave whose distribution at each point in space is the algebraic or vector sum of disturbances at that point resulting from each interfering wave.)

Following observations could not explained by electromagnetic theory of 19th century physics (known as classical physics):
(i) the nature of emission of radiation from hot bodies (black -body radiation)
(ii) ejection of electrons from metal surface when radiation strikes it (photoelectric effect)
(iii) variation of heat capacity of solids as a function of temperature
(iv) line spectra of atoms with special reference to hydrogen.

(1) The black body radiation was given by Max Planck in 1900. When solids are heated they emit radiation over a wide range of wavelengths. For example, If an iron rod is heated in a furnace, it first turns to dull red and then progressively becomes more and more red as the temperature increases. As this is heated further, the radiation emitted becomes white and then becomes blue as the temperature becomes very high.
In terms of frequency, it means that the radiation emitted goes from a lower frequency to a higher frequency as the temperature increases. The red colour lies in the lower frequency region while blue colour belongs to the higher frequency region of the electromagnetic spectrum.
The ideal body, which emits and absorbs all frequencies, is called a black body.
and the radiation emitted by such a body is called black body radiation.
The above experimental results cannot be explained by wave theory of light.
Planck suggested that atoms and molecules could emit (or absorb) energy only in discrete quantities (definite energy packets) and not in a continuous manner.
Planck gave the name quantum to the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation.
The energy (E ) of a quantum of radiation is proportional to its frequency (n ) and is expressed by equation The proportionality constant, ‘h’ is known as Planck’s constant and has the value 6.626× 10–34 J s.

(2) Photoelectric Effect In 1887, H. Hertz gave this phenomenon.
Electrons (or electric current) were ejected when certain metals (for example potassium, rubidium, caesium etc. i.e. metals with low ionisation energy) were exposed to a beam of light. This phenomenon is called Photoelectric effect. , And liberating electrons are known as photo electronsThe results observed in  this experiment were:
(i) The electrons are ejected from the metal surface as soon as the beam of light strikes the surface
(ii) The number of electrons ejected is proportional to the intensity or brightness (no. of energy packets i.e. photons) of light
 Photoelectric effect. Light of a particular frequency strikes a clean metal surface inside a vacuum chamber. Electrons are ejected from the metal and are counted by a detector that measures their kinetic energy.
.(iii) For each metal, there is a minimum frequency,’ν0’ known as threshold frequency is required to eject out an electron. 
OR there is a maximum wavelength, known as threshold wavelength is required to eject out an electron.
At a frequency ν >ν0, the ejected electrons come out with certain kinetic energy.
And if frequency ν <ν0, the electrons can not be ejected.
At a frequency ν =ν0, the ejected electrons come out without kinetic energy
Einstein (1905) explained the photoelectric effect with the help of Planck’s quantum theory of electromagnetic radiation
When a photon of sufficient energy strikes an electron in the atom of the metal, it transfers its energy immediately to the electron during the collision and the electron is ejected without any delay. Greater the energy possessed by the photon, greater will be transfer of energy to the electron and greater the kinetic energy of the ejected electron. Hence kinetic energy of the ejectedelectron is proportional to the frequency of the electromagnetic radiation.
Since the striking photon has energy equal to hn andthe minimum energy required to eject the electron is hn0 known as work function, W0’ then the difference in energy (hν – hν0) is transferred as the kinetic energy of the photo electron. i.e. ‘Law of lowing the conservation of energy’ Here me is the mass of the electron and v is the velocity associated with the ejected electron. No. of ejected electrons/photo electrons are directly proportional to the intensity of incident light radiation.
Dual Behaviour of Electromagnetic Radiation (e.g. Light)
Light shows both particle and wave-like properties, i.e., light has dual behavior. It could explain the black body radiation and photoelectric effect, i.e. Particle like nature and wave nature interference and diffraction.
Some microscopic particles like electrons also exhibit this wave-particle duality. (Cathode rays experiment)
Evidence for the quarantined Electronic Energy Levels: Atomic spectra
The speed of light depends upon the nature of the medium through which it passes. As a result, the beam of light is deviated or refracted from its original path as it passes from one medium to another.
We know when a ray of white light is passed through a prism, the wave with shorter wavelength bends more than the one with a longer wavelength. Since ordinary white light consists of waves with all the wavelengths in the visible range, a ray of white light is spread
out into a series of coloured bands called spectrum. The light of red colour which has longest wavelength is deviated the least while the violet light, which has shortest wavelength is deviated the most. The spectrum of white light, that we can see, ranges from violet at 7.5 x 1014Hz to red at 4 x 1014 Hz. Such a spectrum is called continuous spectrum (i.e. having rays of all possible frequencies so in Continuous spectrum violet merges into blue, blue into green and so on, e.g.a rainbow forms in the sky.
When electromagnetic radiation interacts with matter, (electrons of) atoms and molecules may absorb energy and reach to a higher energy state. With higher energy, these are in an unstable state. For returning to their normal (more stable, lower energy states) energy state, the atoms and molecules emit radiations in various regions of the electromagnetic spectrum.
Emission and Absorption Spectra
The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum. Atoms, molecules or ions that have absorbed radiation are said to be “excited.
To produce an emission spectrum, energy is supplied to a sample by heating it or irradiating by electricity, the wavelength (or frequency) of the radiation emitted by the sample is recorded.
An absorption spectrum is like the photographic negative of an emission spectrum. For a absorption spectrum of a given sample A continuum radiation is passed through given sample, which absorbs radiation of certain wavelengths. The missing wavelength which corresponds to the radiation absorbed by the matter, leave dark spaces in the bright continuous spectrum.
The study of emission or absorption spectra is referred to as spectroscopy.
The spectrum of the visible light has a continuous spectrum as all wavelengths (red to violet) of the visible light are represented in the spectra.
The emission spectra of atoms in the gas phase, emit light only at specific wavelengths with dark spaces between them. Such spectra are called line spectra or atomic spectra because the emitted radiation is identified by the presence of bright lines in the spectra.( The absorption spectrum of same atom also will be the line spectrum) 
Significance of Line emission spectra
Each element has a unique line emission spectrum. The characteristic lines in atomic spectra are used in chemical analysis, to identify unknown atoms in the same way as finger prints are used to identify people. 
The exact matching of lines of the emission spectrum of the atoms of a known element with the lines from an unknown sample gives the identification of the unknown sample.
German chemist, Robert Bunsen (1811-1899) was one of the first investigators to use line spectra to identify elements, like rubidium (Rb), caesium (Cs) thallium (Tl), indium (In), gallium (Ga) and scandium (Sc) were discovered when their minerals were analysed by spectroscopic methods. The element helium (He) was discovered in the sun by spectroscopic method.
Line Spectrum of Hydrogen
When an electric discharge is passed through gaseous hydrogen, the H2 molecules dissociate and the energetically excited hydrogen atoms start to 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 wave number  then the visible lines of the hydrogen spectrum obey the following formula :
here 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. These are the only lines in the hydrogen spectrum which appear in the visible region of the electromagnetic spectrum.
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, n1 + 2...... The value 109,677 cm–1is called the Rydberg constant for hydrogen.
The first 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 given below shows the series of transitions in the hydrogen spectrum. 

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, i.e.,
(i) line spectrum of element is unique and
(ii) there is regularity in the line spectrum of each element.

Q. What are the reasons for these similarities?
---We get answer of this question in understanding electronic structure of these elements.

Neil's Bohr (1913) was the first to explain quantitatively the general features of hydrogen atom structure and its spectrum. it can be used to rationalise many points in the atomic structure and spectra.

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. According to the Table ,The Spectral Lines for Atomic Hydrogen electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed by the electron and energy is emitted when electron moves from higher stationary state to lower stationary state. The energy change does not take place in a continuous manner.
(Angular Momentum -- Just as linear momentum is the product of mass (m) and linear velocity (v), angular momentum is the product of moment of inertia (I) and angular velocity (w). For an electron of mass me, moving in a circular path of radius r around the nucleus,
angular momentum = I x w Since I = mer2 , and w = v/r where v is the linear velocity,
angular momentum = mer2x v/r = mevr

iii) The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by DE, is given by :
Where E1 and Eare 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
Thus an electron can move only in those orbits for which its angular momentum is integral multiple of h/2p, Hence certain fixed orbits are allowed to move an electron.
Derivation of energies of the stationary states-- 
according to Bohr’s theory for hydrogen atom:
a) The stationary states for electron are numbered n = 1,2,3.......... These integral numbers are known as Principal quantum numbers.
b) The radii of the stationary states are expressed as :
where a0 = 52.9 pm. Thus the radius of the first stationary state, called the Bohr radius, is 52.9 pm.
c) The energy of electron, in its stationary state, is given by the expression.
where RH is called Rydberg constant and its value is 2.18 x 10–18 J. The energy of the lowest state, also called as the ground state, is
The energy of the stationary state for n = 2, will be :
Above figure depicts the energies of different stationary states or energy levels of hydrogen atom. This representation is called an energy level diagram.

(Q. What does the negative electronic energy (En) for hydrogen atom mean?

Ans. The energy of the electron in a hydrogen atom has a negative sign for all possible orbits. This negative sign means that the energy of the electron in the atom is lower than the energy of a free electron at rest. A free electron at rest is an electron that is infinitely far away from the nucleus and is assigned the energy value of zero. As the electron gets closer to the nucleus (as n decreases), En becomes larger in absolute value and more and more negative. The most negative energy value is given by n=1 which corresponds to the most stable orbit. We call this the ground state.)
d) Bohr’s theory can also be applied to the ions containing only one electron, similar to that present in hydrogen atom. For example, He+ Li 2+, Be 3+and so on. The energies of the stationary states associated with these kinds of ions (also known as hydrogen like species) are given by the expression. and radii by the expression
where Z is the atomic number and has values 2, 3 for the helium and lithium atoms respectively. From the above equations, it is evident that the value of energy becomes more negative and that of radius becomes smaller with increase of Z . This means that electron will be tightly bound to the nucleus.
e) The velocities of electrons moving in these orbits,--- qualitatively the magnitude of velocity of electron increases with increase of positive charge on the nucleus and decreases with increase of principal quantum number.
Explanation of Line Spectrum of Hydrogen
According to Bohr’s model.---- assumption 2, radiation (energy) is absorbed if the electron moves from the orbit of smaller Principal quantum number to the orbit of higher Principal quantum number, whereas the radiation (energy) is emitted if the electron moves from higher orbit to lower orbit. The energy gap between the two orbits is given by equation
By writing the energy of Ef and Ei
(where ni and nfstand for initial orbit and final orbits)
The frequency (n ) associated with the absorption and emission of the photon can be evaluated by using following equation
In case of absorption spectrum, nf > ni and the term in the parenthesis is positive and energy is absorbed. On the other hand in case of emission spectrum ni > nf , D E is negative and energy is released.
Each spectral line, whether in absorption or emission spectrum, can be associated to the particular transition in hydrogen atom. In case of large number of hydrogen atoms, different possible transitions can be observed and thus leading to large number of spectral lines. The brightness or intensity of spectral lines depends upon the number of photons of same wavelength or frequency absorbed or emitted.
Limitations of Bohr’s Model
i) It fails to explain the finer details (doublet, that is two closely spaced lines) of the hydrogen atom spectrum.
ii) It is unable to explain the spectrum of atoms other than hydrogen, for example, helium atom which possesses only two electrons.
iii) It fails to explain the splitting of spectral lines in the presence of magnetic field (Zeeman effect) or an electric field (Stark effect).
ii) It could not explain the ability of atoms to form molecules by chemical bonds.

It is formulated with the help of two theories--
1. Dual behaviour of matter,
2. Heisenberg uncertainty principle.

Dual Behaviour of Matter
The French physicist, de Broglie in 1924 proposed that matter, like radiation, exhibits dual behaviour i.e., both particle and wavelike properties. It means the photon has momentum as well as wavelength, electrons also have momentum as well as wavelength, de Broglie, gave the following relation between wavelength (l) and momentum (p) of a material particle.
Here m is the mass of the particle, v its velocity and p its momentum. de Broglie’s prediction was confirmed experimentally that --
(1) An electron beam undergoes diffraction, a phenomenon
characteristic of waves.
Electron microscope works at this principle, which is based on the wavelike behaviour of electrons just as an ordinary microscope utilises the wave nature of light.
An electron microscope is a powerful tool in modern scientific research because it achieves a magnification of about 15 million times.
----According to de Broglie, every object in motion has a wave character. The wavelengths associated with ordinary objects are so short (because of their large masses) that their wave properties cannot be detected. 
The wavelengths associated with electrons and other subatomic
particles (with very small mass) can be detected experimentally.

Heisenberg’s Uncertainty Principle
Werner Heisenberg a German physicist in 1927, stated uncertainty principle which is the consequence of dual behaviour of matter and radiation. It states that
it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.’ Mathematically, it can be given as
where Dx is the uncertainty in position and Dpx ( or Dvx) is the uncertainty in momentum (or velocity) of the particle.
To observe an electron, we have to illuminate it with “light” or electromagnetic radiation. The “light” used must have a wavelength smaller than the dimensions of an electron. The high
momentum photons of such light (p= h/n) would change the energy of electrons by collisions. In this process we can’t calculate the position of the electron and its velocity.
Significance of Uncertainty Principle
1. It rules out existence of definite paths or trajectories of electrons and other similar particles.
(The effect of Heisenberg Uncertainty Principle is significant only for motion of microscopicobjects and is negligible for that of macroscopic objects, e.g. .If uncertainty principle is applied to an object of mass 1 milligram (10–6 kg), then
The value of ΔvΔx is extremely small and is insignificant. Therefore, one may say that in dealing with milligram-sized or heavier objects, the associated uncertainties are hardly of any real consequence.
In the case of a microscopic object like an electron, Δv.Δx obtained is much larger and such uncertainties are of real consequence. For example, for an electron whose mass is 9.11× 10–31 kg., according to Heisenberg uncertainty principle
It, means that if one tries to find the exact location of the electron, an uncertainty of only 10–8m, then the uncertainty Δv in velocity would be
which is so large that the classical picture of electrons moving in Bohr’s orbits (fixed) cannot hold good.
Hence the precise statements of the position and momentum of electrons replaced by the statements of probability, This is the quantum mechanical model of atom.

Reasons for the Failure of the Bohr Model
1. The wave character of the electron is not considered in Bohr model.
2. It ignores dual behaviour of matter.
Due to these weaknesses in the Bohr model, It is not extended to other atoms.

Classical mechanics, based on Newton’s laws of motion, fails when applied to microscopic objects like electrons, atoms, molecules etc. because it ignores the concept of dual behaviour of matter and the uncertainty principle.
The branch of science based on dual behaviour of matter is called quantum mechanics.
Quantum mechanics is a theoretical science that deals with the study of the motions of the microscopic objects that have both observable wave like and particle like properties.
Quantum mechanics was developed independently in 1926 by Werner Heisenberg and Erwin Schrödinger. Here, we are discussing the quantum mechanics which is based on the wave motion.
The fundamental equation of quantum mechanics was developed by Schrödinger and it won him the Nobel Prize in Physics in 1933.
For a system (such as an atom or a molecule whose energy does not change with time) the Schrödinger equation is written as where H is a mathematical operator called Hamiltonian Operator, E is total energy of the system (i.e. kinetic energies of all the sub-atomic particles (electrons, nuclei), attractive potential between the electrons and nuclei and repulsive potential among the electrons and nuclei e.t.c.)

Hydrogen Atom and the Schrödinger Equation
The solutions of Schrödinger equation for hydrogen atom, gives the possible energy levels of electron and the corresponding wave function Ψof the electron associated with each energy level. These quantized energy states and corresponding wave functions are characterized by a set of three quantum numbers (principal quantum number n, azimuthal quantum number l and magnetic quantum number ml )
Significance of the wave functionThe wave function (Ψ ) for an electron in an atom has no physical significance.
(Ψ2 ) at any point gives the probability of finding the electron at that point i.e. electron density at that point.

Electron cloudThe region of space around the nucleus which describes the probability of finding an electron of given energy in terms of dots is called an electron cloud.
Atomic Orbital—It is three dimensional space around the nucleus where electron finding probability is maximum.
Difference between orbit and orbital
1. It is well defined circular path around the nucleus in which electron revolves It is three dimensional space around the nucleus where electron finding probability is maximum.
2. It represents the planar motion of electron around the nucleus. It represents the 3-D motion of electron around the nucleus.
3. The concept of an orbit is not accordance with the wave nature of electron and uncertainity principal. The concept of an orbit is in accordance with the wave nature of electron and uncertainity principal
4. All orbits are circular, concentric and disc like. Different orbitals have different shapes.
5. They don’t have directional properties. They all except s-orbitals have directional properties.
6. The maximum no of electrons in any orbit is given by 2n2 Only two electrons can reside in any orbital.

Important Features of the Quantum Mechanical Model of Atom
The following are the important features of the quantum mechanical model of atom:

1. The energy of electrons in atoms is quantized (i.e., can only have certain specific values)

2. The existence of quantized electronic energy levels is a direct result of the wave like properties of electrons and are allowed solutions of Schrödinger wave equation.

3. Both the exact position and exact velocity of an electron in an atom cannot be determined simultaneously (Heisenberg uncertainty principle).
The path of an electron in an atom therefore, can never be determined or known accurately.

4. An atomic orbital is the wave function y for an electron in an atom. In each orbital, the electron has a definite energy. An orbital cannot contain more than two electrons.
In a multi-electron atom, the electrons are filled in various orbitals in the order of increasing energy.
(All the information about the electron in an atom is stored in its orbital wave functionΨ and quantum mechanics makes it possible to extract this information out of Ψ.)

5. The probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function i.e., | Ψ|2 at that point. |y|2 is known as probability density and is always positive.From the value of | Ψ|2 at different points within an atom, it is possible to predict the region around the nucleus where electron will most probably be found.

Orbitals and Quantum Numbers
Qualitatively orbitals can be distinguished by their size, shape and orientation Atomic orbitals are precisely distinguished by quantum numbers. Each orbital is designated by three quantum numbers labelled as n, l and m/ml.
1. The principal quantum number ‘n’--- is a positive integer with value of n = 1,2,3....... .
1. It determines the size and energy of the orbital.., Size and energy of an orbital will increase with increase of principal quantum number ‘n’
2. It identifies the shell/orbit.
3. Total no. of orbitals in nthorbit will be n2. 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.
2. Azimuthal quantum number. ‘l’ or orbital angular momentum or subsidiary quantum number.----
1. It defines the three dimensional shape of the orbital.
2. For a given value of n, l have n 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 can be 0 and 1. For n = 3, the possible l values are 0, 1 and 2.
3. Each shell consists of one or more subshells or sub-levels. The number of subshells 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. There are two sub-shells (l = 0, 1) in the second shell (n = 2), three (l = 0, 1, 2) in third shell (n = 3) and so on. Each sub-shell is assigned an azimuthal quantum number (l ). Sub-shells corresponding to different values of l are represented by the following
symbols. Value for l : 0 1 2 3 4 5 ............
notation for s p d f g h ............
Following Table shows the permissible values of ‘l ’ for a given principal quantum number and the corresponding sub-shell notation.
n = 1 Than l = 0 Sub shell notation --- 1s
n = 2 Than l = 0 , 1 sub shell notation --- 2s , 2p respectively
n = 3 Than l = 0 , 1, 2, sub shell notation --- 3s , 3p , 3d respectively.
3. Magnetic orbital quantum number. ‘ml
1. it tells about the orbitals.
2. It gives information about the spatial orientation of the orbital with respect to standard set of co-ordinate axis. For any sub-shell (defined by ‘l’ value) Total possible values of ml are 2l+1 and these values are designated as : ml
= – l, to +l through 0. Thus for l = 0, the only permitted value of
ml = 0, [2(0)+1 = 1, one s orbital]. For l = 1, ml can be –1, 0 and +1 [2(1)+1 = 3, three p orbitals]. For l = 2, ml = –2, –1, 0, +1 and +2, [2(2)+1 = 5, five d orbitals].
[note-- The values of ml are derived from l and that the value of l are derived from n. Each orbital in an atom, therefore, is defined by a set of values for n, l and ml.]
e.g. An orbital described by the quantum numbers n = 2, l = 1, ml = 0, It will be 2ndorbital of 2p.
The following chart gives the relation between the sub-shell and the number of orbitals associated with it.
Hence above three quantum no.s are the solution of Schrodinger equation and define energy, shape and orientation of an an atomic orbital. 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. In 1925, George Uhlenbeck and SamuelGoudsmit proposed the presence of the fourth quantum number known as the electron spin quantum number (ms).
Electron spin ‘s’ :
An electron spins around its own axis, In other words, an electron has, besides charge and mass, intrinsic spin angular quantum number. 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 +½ or –½. 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 +½ and the other –½) are said to have opposite spins.
Hence An orbital cannot hold more than two electrons and these two electrons should have opposite spins.
Shapes of Atomic Orbitals-
Shape of ‘s’-orbital-- According to the German physicist, Max Born, the square of the wave function(i.e.,Ψ2) at a point gives the probabilitydensity of the electron at that point. The
variation of Ψ2as a function of r for 1s and 2s orbitals is given in Fig.
Fig. The plots of the variation of probability density Ψ2(r) as a function of distance r of the electron from the nucleus for 1s and 2s orbitals.
Here the curves for 1s and 2s orbitals are different. For 1s orbital the probability density is maximum at the nucleus and it decreases sharply as we move away from it. On the other hand, for 2s orbital the probability density first decreases sharply to zero and again starts increasing. After reaching a small maxima it decreases again and approaches zero as the value of r increases further.
The region where this probability density function (i.e. electron finding probability) reduces to zero is called nodal surfaces or simply nodes.
In general, ns-orbital has (n – 1) nodes, i.e. number of nodes for 2s orbital is one, two for 3s and so on.
These probability density variation can be visualised in terms of charge cloud diagrams [Fig.(a)]. In these diagrams, the density of the dots in a region represents electron probability density in that region. Boundary surface diagrams of constant probability density for different orbitals give a representation of the shapes of the orbitals. In this representation, a boundary surface is drawn in space for an orbital on which the value of probability density Ψ2is constant. In principle many such boundary surfaces may be possible. However, for a given orbital, only that boundary surface diagram of constant probability density* is taken to be good representation of the shape of the
orbital which encloses a region or volume in which the probability of finding the electron is very high, say, 90%. . The density of the dots represents the probability density of finding the electron in that region. (b) Boundary surface diagram for 1s and 2s orbitals.
All the s-orbitals are spherically symmetric, that is, the probability of finding the electron at a given distance is equal in all the directions. The size of s orbital increases with increase in n, that is, 4s > 3s > 2s > 1s and the electron is located further away from the nucleus as the principal quantum number increases.
Shape of p- orbitals
Boundary surface diagrams for three 2p orbitals (l = 1)
In these orbitals the nucleus is at the origin. Here each p orbital consists of two sections called lobes that are on either side of the plane that passes through the nucleus. The probability density function is zero on the plane where the two lobes touch each other. The size, shape and energy of the three orbitals are identical. They differ in orientation. Since the lobes may be considered to lie along the x, y or z axis, they are designated as 2px, 2py, and 2pz. But there is no relation between the values of ml(–1, 0 and +1) and the x, y and z directions. These three p orbitals have mutually perpendicular axes. They also increase in size and energy with increase in the principal quantum number and hence the order of the energy and size of various p orbitals is 4p > 3p > 2p. Like s orbitals, the probability density functions for p-orbital also pass through value zero,The number of radial node are given by the n –2. Hence there is 1 radial node for 3p orbital, two for 4p orbital and so on.
Shape of d-orbital-

The five d-orbitals are designated as dxy, dyz, dxz, dx2–y2and dz2. The shapes of the first four d-orbitals are similar to each other, where as that of the fifth one, dz2, is different from others, but all five 3d orbitals are equivalent in energy. The d orbitals for which n is greater than 3 (4d, 5d...) also have shapes similar to 3d orbital, but differ in energy and size.
Angular nodes--
Besides the radial nodes (i.e., probability density function is zero), the probability density functions for the np and nd orbitals are zero at the plane (s), passing through the nucleus (origin). For example, in case of pz orbital, xy-plane is a nodal plane, in case of dxy orbital, there are two nodal planes passing through the origin and bisecting the xy plane containing z-axis. These are called angular nodes and number of angular nodes are given by ‘l’, i.e., one angular node for p orbitals, two angular nodes for ‘d’ orbitals and so on. The total number of nodes are given by (n–1), i.e., sum of l angular nodes and (n – l – 1) radial nodes.
Note—All d-orbitals have two nodal plane, except dz2which has no nodal plane.
Energies of Orbitals
The energy of an electron in a hydrogen atom is determined solely by the principal quantum number b/c it has only one electron. Thus the energy of the orbitals increases as follows :
1s < 2s = 2p < 3s = 3p = 3d <4s = 4p = 4d = 4f <
The orbitals having the same energy are called degenerate.
---In multi-electronic atoms, the main reason for having different energies of the subshells is the mutual repulsion among the electrons.
---Besides the presence of attraction between the electron and nucleus, there are repulsion between every electron and other electrons present in the atom. Thus the stability of an electron in multi-electron atom is because total attractive interactions are more than the repulsive interactions.
----The attractive interactions of an electron increases with increase of positive charge (Ze) on the
nucleus. Due to the presence of electrons in the inner shells, the electron in the outer shell will not experience the full positive charge on the nucleus (Ze), but will be lowered due to the partial screening of positive charge on the nucleus by the inner shell electrons. This is known as the shielding of the outshellelectrons from the nucleus by the inner shell electrons, and the net positive charge experienced by the electron from the nucleus is known as effective nuclear charge(Zeffe).
(Despite the shielding of the outer electrons from the nucleus by the inner shell electrons, the attractive force experienced by the outer shell electrons increase with increase of nuclear charge. In other words, the energy of interaction between, the nucleus and electron (that is orbital energy) decreases (that is more negative) with the increase of atomic number (Z).
---Due to spherical shape, s orbital electron spends more time close to the nucleus in comparison to p orbital and p orbital spends more time in the vicinity of nucleus in comparison to d orbital, i.e. for a given shell (principal quantum number), the Zeff experienced by the orbital decreases with increase of azimuthal quantum number (l), thus, the s orbital will be more tightly bound to the nucleus than p orbital and p orbital in turn will be better tightly bound than the d orbital. The energy of s orbital will be lower (more negative) than that of p orbital and that of p orbital will be less, than that of d orbital and so on. Since the extent of shielding of the nucleus is different for different orbitals, it leads to the splitting of the energies of the orbitals within the same shell (or same principal quantum number), i.e., energy of the orbital, depends upon the values of n and l. ---------Mathematically, the energies of the orbitals given by (n + l) rule.
1.The lower the value of (n + l) for an orbital, the lower is its energy.
2. If two orbitals have the same value of (n + l), the orbital with lower value of n will have the lower energy.
-----Lastly it may be mentioned here that energies of the orbitals in the same sub shell decrease with increase in the atomic number (Zeff), e.g. energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium and that of lithium is greater than that of sodium and so on i.e. E2s(H) >E2s(Li) > E2s(Na) > E2s(K).
Filling of Orbitals in Atom “aufbau principlewhich is based on the Pauli’s exclusion principle, the Hund’s rule of maximum multiplicity and the relative energies of the orbitals.
Aufbau Principle--The word ‘aufbau’ in German means ‘building up’. The building up of orbitals means the arrangement of Orbitals withIncreasing Energy on the basis of(n+l ) Rule
filling up of orbitals with electrons.
The order in which the energies of the orbitals increase and hence the order in which the orbitals are filled is as follows :
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s...
Pauli Exclusion Principle
Given by the Austrian scientist Wolfgang Pauli (1926). According to this principle : No two electrons in an atom can have the same set of four quantum numbers. OR “Only two electrons may exist in the same orbital and these electrons must have opposite spin.” i.e. that the two electrons can have the same value of three quantum numbers n, l and ml, than 4thwill be different. ---It helps in calculating the capacity any subshell, e.g.subshell 1s comprises of one orbital and thus the maximum number of electrons present in 1s subshell can be two, in p and d subshells, the maximum number of electrons can be 6 and 10 and so on.
----This can be summed up as : the maximum number of electrons in the shell with principal
quantum number n is equal to 2n2.
Hund’s Rule of Maximum Multiplicity
This rule deals with the filling of electrons into the orbitals belonging to the same subshell (i.e. orbitals of equal energy, called degenerate orbitals). It states : pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each i.e., it is singly occupied. Since there are three p, five d and seven f orbitals, therefore, the pairing of electrons will start in the p, d and f orbitals with the entry of 4th, 6th and 8thelectron, respectively.
--- Half filled and fully filled degenerate set of orbitals acquire extra stability due to their symmetry
Electronic Configuration of Atoms
The distribution of electrons into orbitals of an atom is called its electronic configuration.
The electronic configuration of different atoms can be represented in two ways.
----The advantage of second notation over the first is that it represents all the four quantum numbers.
-- The electronic configuration of the hydrogen atom is 1s1, helium (He) 1s2,lithium (Li) 1s22s1, beryllium (Be)-1s22s2, boron (B, 1s22s22p1), carbon (C, 1s22s22p2), nitrogen (N, 1s22s22p3), oxygen (O, 1s22s22p4), fluorine (F, 1s22s22p5) and neon (Ne, 1s22s22p6).
--The orbital picture of these elements can be represented as follows :
---This process can be simplified if we represent the total number of electrons in the first two shells by the name of element neon (Ne). The electronic configuration of sodium can be written as (Na, [Ne]3s1)
---The electrons in the completely filled shells are known as core electrons and the electrons that are added to the electronic shell with the highest principal quantum number are called valence electrons. e.g. the electrons in Ne are the core electrons and rest are the valence electrons.

Q. What is the utility of knowing the electron configuration?
Ans. The modern approach to the chemistry, infact, depends almost entirely on electronic distribution to understand and explain chemical behaviour.
Q. Why two or more atoms combine to form molecules?
Q. Why some elements are metals while others are nonmetals?
Q. Why elements like helium and argon are not reactive but elements like the halogens are reactive, (Hint: due to electronic configuration.)

Stability of Completely Filled and Half Filled Subshells
The ground state electronic configuration of the atom of an element always corresponds to the state of the lowest total electronic energy. In certain elements such as Cu, or Cr, where the two subshells (4s and 3d) differ slightly in their energies, an electron shifts from a subshell of lower energy (4s) to a subshell of higher energy (3d), provided such a shift results in all orbitals of the subshell of higher energy getting either completely filled or half filled. The valence electronic configurations of Cr and Cu, therefore, are 3d54s1and 3d104s1respectively and not 3d44s2and 3d94s2. It has been found that there is extra stability associated with these Completely Filled and Half Filled Sub-shells
The completely filled and completely half filled sub-shells are stable due to the following reasons:-----
1.Symmetrical distribution of electrons: It is well known that symmetry leads to stability. The completely filled or half filled sub shells have symmetrical distribution of electrons in them and are therefore more stable. Electrons in the same sub shell (here 3d) have equal energy but different spatial distribution. Consequently, their shielding of one another is relatively small and the electrons are more strongly attracted by the nucleus.
2. Exchange Energy : The stabilizing effect arises whenever two or more electrons with the same spin are present in the degenerate orbitals of a subshell. These electrons tend to exchange their positions and the energy released due to this exchange is called exchange energy. The number of exchanges that can take place is maximum when the subshell is either half filled or completely filled. As a result the exchange energy is maximum and so is the stability.
i.e. Hund’s rule based on exchange energy that electrons which enter orbitals of equal energy have parallel spins as far as possible.
Hence, the extra stability of half-filled and completely filled sub shell is due to:
(i) relatively small shielding, (ii) smaller coulombic repulsion energy, and

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