Atomic Structure

Atomic Structure Mock Tests for self assessment Test 1 | Test 2 | Test 3 |


• 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.
• The atomic theory of matter was first proposed on a firm scientific basis by John Dalton.
• His theory, called Dalton’s atomic theory, regarded the atom as the ultimate particle of matter.
• Atom is the smallest particle of matter which can directly take part in chemical reactions. It has no independent existence.
• The term “ Atom “ was first used by John Dalton

• Dalton’s Theory is able to explain law of conservation of mass, law of constant composition and law of multiple proportions
• Dalton’s law is failed to explain the experiments like when glass or ebonite rubbed with silk or fur generate electricity
• Above experiment indicates that there is a presence of subatomic particles like electron, neutron, proton are present in the atom

• Electrons, protons and neutrons are the fundamental particles of atom.
• Protons and neutrons are present in the nucleus and are collectively called nucleons.
• Electrons are the negatively charged particles with unit charge and negligible mass.
• Protons are positively charged particles with unit mass.
• Neutrons are the neutral particles with unit mass.


Electron –1.6022 x 10-19 coulomb

4.802 x 10-10  e.s.u

1 unit ‘-’ charge

9.10939 x 10-31 kg

9.10939 x 10-28 g

0.00054 a.m.u

1/1837th part of weight of one H atom

Proton +1.6022 x 10-19 coulomb (S.I.)

+4.802 x 10-10 esu (C.G.S.)

1 unit ‘+’ charge

1.67262 x 10-27 kg

1.67262 x 10-24 g

1.00727 a.m.u.

Neutron zero 1.67493 x 10-27 kg

1.67493 x 10-24 g

1.00867 a.m.u.

• Charge of one mole of Electrons  = 96,500 C
= 1 Faraday
• mass of one mole of Electrons      = 0.55 mg
e/m value of electron                        = 1.759 x 108 C/g
= 1.759 x 1011 C/kg (or) 5.28 x 1017 esu/g
• Mass of one mole protons              = 1.007 g
e/m value of proton                            = 9.58 x 104 C/g
• Mass of one mole neutron               = 1.008 g

• In mid 1850s many scientists mainly Faraday began to study electrical discharge in partially evacuated tubes, known as cathode ray discharge tubes.
• Atomic structure was obtained from the experiments on electrical discharge through gases.
• During the discharge tube experiments “Crookes” observed that rays were found to pass from negatively charged filament (cathode) to positively charged plate (anode).
• By maintaining low pressure and high voltage in discharge tube current or stream of particles moving in the tube from cathode to anode.
• Those rays are known as 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.

• Cathode rays starts from cathode and move towards anode
• Rays travel straight lines in the absence of electric and magnetic field
• In the presence of electric and magnetic field they are deflected indicates that cathode rays contain negatively charged particles known as electrons
• Cathode rays found to be independent of nature of the cathode material and nature of the gas in the tube.

• J.J. Thomson measured e/m ratio of the electron based on following points
• Greater the magnitude of the charge on the particle greater is the deflection when electric and magnetic field is applied.
• Lighter the mass of the particle greater will be deflection.
• The deflection of electrons from its original path increases when voltage increases from the above points Thomson was able to determine the value of charge to mass ratio as 1.758820 × 1011 C kg–1

• e/m of electron is constant

• Mullikan determined the charge of the electron by an oil drop experiment
• By carefully measuring the effects of the electrical field on the movement of many droplets.
• Charge on the oil drops was always an integral multiple of 1.60 x 10–19 C

= 9.1094 x 10–31 kg
• Electrons are universal constituents of all matter.

Proton : Discovered by Gold Stein, he used perforated cathode in the discharge tube and repeated Thomson experiment and observed the formation of anode rays. These rays also termed as positive or Canal rays.

• Anode rays travel in straight line, and these are material particles.
• Anode rays are positively charged, and get deflected by external magnetic field and affect the photographic plate.
• e/m value of these rays is smaller than that of electrons.
• e/m value of anode rays depends upon nature of the gas.
• e/m value of anode rays is maximum when the gas present in the tube is hydrogen.
• By the dissociation and ionization of hydrogen under low pressure discovered with charge +1 and mass 1, particles are called protons.

NEUTRON: Neutron was discovered by James Chadwick based on nuclear reaction, by bombarding a thin layer (sheet) of beryllium by particles neutral particles neutral particles having mass slightly greater than that of protons was emitted particles are named as Neutrons.
Millikan’s Oil Drop Method
• In this method, oil droplets in the form of mist produced by the atomizer, were allowed to enter through a tiny hole in the upper plate of electrical condenser
• The downward motion of these droplets was viewed through the telescope, equipped with a micrometer eye piece.
• By measuring the rate of fall of these droplets, Millikan was able to measure the mass of oil droplets.
• The air inside the chamber was ionized by passing a beam of X-rays through it.
• The electrical charge on these oil droplets was acquired by collisions with gaseous ions.
• The fall of these charged oil droplets can be retarded, accelerated or made stationary depending upon the charge on the droplets and the polarity and strength of the voltage applied to the plate.
• By carefully measuring the effects of electrical field strength on the motion of oil droplets.
• Millikan concluded that the magnitude of electrical charge, q, on the droplets is always an integral multiple of the electrical charge, e, that is q=ne, where n = 1,2,3……

• Although some of these models were not able to explain the stability of atoms, two of these models, proposed by J.J Thomson and Ernet Rutherford are discussed below.
J.J 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.
• Many different names are given to this model, for example, plum pudding, raisin pudding or watermelon.
• An important feature of this model is that the mass of the atom is assumed to be uniformly distributed over the atom.
• Although this model was able to explain the overall neutrality of the atom, but was not consistent with the results of later experiments.


• Wilhalm Roentgen (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 Roentgen did not know the nature of the radiation, he named them X-rays.
• Henri Becqueral 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., a, b- and g-rays are emitted.
• Rutherford found that a-rays consist of high energy particles carrying two units of positive charge and four units of atomic mass.

• Rutherford proposed atomic model based on a-ray scattering experiment
• Scattering of a narrow beam of a-particles as they passed through a thin gold foil and it is covered with fluorescent ZnS screen.
• When a-particles struck the screen then flash of light was produced at that point.

• Most of the a-particles passes through the foil un-deflected.
• A small fraction of a- particles were deflected by small angles.
• A very few a-particles bounced back were deflected by 1800

• Most of the space in the atom is empty
• A few positive charges were deflected the deflection must be due to enormous repulsive forces showing that the positive charge of the atom is not spread out the atom.

• All the positive charge and mass of the atom is present in a very small region at the center of the atom. It is called nucleus.
• The size of the nucleus is very small in comparison of the size of the atom.
• Most of the space outside the nucleus is empty.
• The electrons revolve round the nucleus like planets revolve round the sun.
• The centrifugal force arising due to fast moving electrons balances the Coulomb force of attraction of the nucleus and the electrons.
• Rutherford’s atomic model is comparable with the solar system. So it is called planetary model.

• It is against to law of electrodynamics.
• It fails to explain the atomic spectrum or line spectrum.

• A neutral atom contains equal number of electrons and protons.
• Mosley discovered the relationship between frequencies of the characteristic X-rays of an element and its atomic number.

Z is a characteristic specific to an element later it was named as atomic number.
 is the frequency of characteristic X- rays.
• a = proportionality constant

b = screening constant
• These values are different for different elements.
• Atomic number was discovered by Mosley
• The number of electrons or protons present in an atom of an element is called its atomic number.
• Atomic number is denoted by Z.
• Atomic number (Z) = number of protons in the nucleus of an atom = number of electrons in a neutral atom
• The sum of protons and neutrons in the atom of an element is called its mass number.
• It is denoted by A.
• mass number (A) = number of protons (Z) + number of neutrons (n)
• Number of neutrons = A – Z .
• Mass number is always a whole number.


• Isotopes : Atoms with identical atomic number but different mass numbers are known as isotopes.
• Isotopes exhibit similar chemical properties.
Eg : 1) Isotopes of hydrogen → 1H1, 1H2, 1H3 Protium, Deuterium, Tritium
2) Isotopes of chlorine → 17Cl35, 17Cl37.
3) Isotopes of Carbon → 6C12, 6C13, 6C14.
Isobars : Atoms with same mass number with different atomic number are known as isobars.
Eg : 6C14, 7N14

• The two theories which explain the propagation of light are (i) wave theory. (ii) corpuscular theory
• Cosmic rays, g-rays, X-rays, UV light, visible light, Infrared light, micro waves, TV waves and radio waves are called electromagnetic radiation because they are made up of electric and magnetic fields propagating in perpendicular directions to one another.
• Electromagnetic radiations have wave characteristics and no medium is required for their propagation. They can travel through the vacuum.
• The vertical component of the wave (E) indicates the variation of electric field strength.
• The horizontal component of the wave (H) indicate the variation of magnetic field strength.
• In the propagation of electromagnetic radiation only the wave moves but not the medium.
• ‘a’ is the amplitude of the wave or intensity of the radiation.
• Height of crest or depth of trough of a wave is amplitude. It is measured in cm (or) m
• The distance between two successive crests or troughs is called the wave length (λ).
• Wavelength is measured in Angstrom units or nano metres.
1A0 = 10-8cm = 10-10 m = 10-1 nm = 10-4 = 102 = 105 Fermi.
1 nm = 10-9 m = 10 A0
• All types of electromagnetic radiations travel in air or in vacuum with 3 x 108 ms-1 or 3 x 1010 cm.s-1 velocity
frequency x wavelength = velocity
νλ = c
• The number of waves that cross a certain point in 1 second is called the frequency of the wave. It is measured in cycle/ sec (or) Hertz (1 cps = 1 Hz)
• The reciprocal of wavelength is called wave number. (or)
Number of wavelengths per centimetre is called wave number
wave number =
The units of wave number is cm-1 or m-1.
Relation between wave characteristics is

• This theory was proposed by Newton. According to this theory, light is propagated in the form of small particles which are invisible
• This theory went into oblivion after the advent of wave theory.
• Planck’s quantum theory successfully explained black body radiation.
• A hollow sphere coated inside with platinum black and having a small hole in its wall acts as a nearly perfect black body.
• A black body is not only a perfect absorbed but also a perfect emitter of radiant energy.
• The radiations emitted by a black body kept at high temperature give a spectrum of different wavelengths.
• Different curves are obtained at different temperatures when the intensity of radiation is plotted against wavelength.
• The study of the curves shows that the nature of the radiation depends on temperature.
• At a given temperature, the intensity of radiation increases with wavelength, reaches a maximum and then decreases.
• As the temperature increases the peak of the curve shifts to lower wavelengths.

• The vibrating particle in the black body does not emit energy continuously.
• It is emitted in the form of small packets called quanta.
• A discrete packet of energy is called quantum.
• The emitted radiant energy is propagated in the form of waves.
• If the vibrating particles oscillate with a frequency ν, then the energy associated with a quantum

h is a constant called Planck’s constant
h = 6.6256 x 10-34 J.s. or kgm2 s-1
= 6.6256 X 10-27 erg.s or gcm2 s-1
= 1.585 x 10–34 cal.sec
• Energy is emitted or absorbed in some simple integral multiples of a quantum.
E = nhν
• This is called quantization of energy.

• Planck’s quantum theory was extended to all types of electromagnetic radiations by Einstein.
• According to Max Planck, energy is emitted in the form of packets and propagated in the form of waves.
• According to Einstein, both emission and propagation of energy take place in the form of photons.
• Energy of photon ∝ frequency of radiation
i.e E ∝ ν

• Einstein explained photoelectric effect with the help of his generalized quantum theory.
• Emission of electrons from the metal surface when it is exposed to light having certain minimum frequency is called photoelectric effect.
• The electrons emitted are called photo electrons. It is observed that violet light is able to eject from potassium but red light has no effect.
• According to Einstein, electron is ejected from a metal when it is struck by a photon which has sufficient energy.

• If the photon has insufficient energy it cannot eject the electron.
• Photon of violet light has higher energy than that of red light.
• When the photon strikes the metal its energy is absorbed by the electron causing the photon to disappear.
• A part of the photon energy is used to free the electron from the attractive forces in the metal and the remaining energy is transformed into the kinetic energy of the released electron.

kinetic energy of photo electrons depends only on the frequency of incident light.
But not on the intensity of light.
Values of work function (W) for a few metals.

• An impression produced on photographic plate when radiation of a particular wavelength is passed through a prism and allowed to fall on a photographic plate is called spectrum
• Apparatus used to record spectrum is called spectroscope (or) spectrometer

• Sun light or light from an incandescent filament lamp gives a continuous spectrum.
• When a gas or a vapour of a metal is kept in a discharge tube and high potential is applied, a line spectrum is formed.
• Each element has its own characteristic line spectrum.
• Line spectrum is characteristic of atoms (Atomic spectrum)
• Band spectrum is characteristic molecules ( Molecular spectrum)
• The spectra obtained by the emission of energy by the excited atoms are called emission spectra.
• These spectra consist of bright lines on the photographic plate having dark background.
• When white light is passed through a gas and the emergent beam of light is allowed to fall on a photographic plate, the spectrum obtained is called absorption spectrum.
· As the substance absorbs certain portion of white light dark lines appear on photographic plate having bright background.
• For a given element dark lines in the absorption spectrum coincide with the bright lines in the emission spectrum.

• The source of radiation here is a hydrogen discharge tube.
• The discharge tube contains hydrogen gas at low pressure and high potential difference.
• The bright light emitted from the discharge tube is passed through a prism to cause dispersion.
• The emergent beam of light falls on a photographic plate and is recorded as the atomic spectrum of hydrogen.
• The hydrogen spectrum is the simplest of all the atomic spectra.
• It contains a number of groups of lines.
• They can be classified into various series. Only one such series is visible to the naked eye and is termed as the visible region of hydrogen spectrum.
• It was discovered by Balmer so, it is called Balmer series.
• The wavelength or wave number of various lines in the visible region can be calculated using equation

where n1 = 2 which is constant for all the lines in Balmer series.
n2 = 3, 4, 5
R is Rydberg constant and its value for hydrogen
is 1,09,677 cm-1 or 1.09677 x 105 cm-1

• The spectra lines get closer when the n2 value is increased.
• If n2 is taken as infinity the wavelength of the limiting line in the series is obtained wave length of limiting line of any series in any hydrogen like species

• The other series in the hydrogen spectrum are invisible.
• The wave length or wave numbers of all the lines in all the series can be calculated by using Rydberg’s equation

• maximum number lines produced when electron jumps from nth level to ground level =


• The value of R = 1,09,678 cm-1 is valid only for the lines in the hydrogen spectrum.
• For a spectral line of anyone electron species like He+, Li2+ the value of R = RH × Z2
• First line in any series is called Hα line
• Second line in any series is called Hß line
• Third line in any series is called Hγ line
• Fourth line in any series is called Hδ line
• Last line in any series is called series limit or limiting line of the series
The no. of spectral lines formed during the deexcitation from

Series limit µ
For ‘H’ atom :

For any species like ‘H’ atom ( He+, Li2+, Be3+)

• Bohr recognised the relationship between the nature of the series of spectral lines and the arrangement of electrons in the atom.- Bohr applied Planck’s quantum theory to the electrons revolving around the nucleus.- Bohr proposed his theory to explain the structure of atom.
• The important postulates of his theory are:
• Electrons revolve around the nucleus with definite velocities in concentric circular orbits.
• These orbits are called stationary orbits as the energy of the electron remains constant.
• As long as electron revolves in the same circular orbit it neither radiates nor absorbs energy.
• Angular momentum = I x w
Where I = moment of inertia
w = angular velocity
I = mer2

• The angular momentum of the electron is quantised. The electronic motion is restricted to those orbits where the angular momentum of an electron is an integral multiple of h/2π or
mvr = nh / 2π. This is called “Bohr’s quantum condition”.
• Energy of the electron changes only when it moves from one orbit to another orbit.
• Energy is absorbed when an electron jumps from an inner orbit to an outer orbit.
• Energy is released when an electron jumps from an outer orbit to inner orbit.
• The released or absorbed energy is equal to the difference between the energies of the two orbits.
• If E2 is the energy of the electron in the outer orbit (n2) and E1 is the energy of the electron in the inner orbit (n1) then E2 – E1 = ΔE = hv .
• With the help of these postulates Bohr derived he expressions for the radius of the circular orbit, energy of the electron in a circular orbit and velocity of the electron in a circular orbit.
• Bohr’s formula could satisfactorily explain the formation of different series of lines in hydrogen spectrum.
• The wavelengths and the frequencies of the lines determined experimentally are in excellent agreement with those calculated by using Bohr’s equation.

• Hydrogen atom contains one proton in the nucleus and one electron revolving around the nucleus in a circular orbit of radius r.
• The electron maintains the same circular orbit when it is subjected to two equal and opposing forces. Centripetal force = centrifugal force

• The radius of the nth circular orbit rn is given by

• The radius of the first orbit of hydrogen atom is called Bohr’s radius which is denoted by r0
r0 = 0.529 × 10-8 cm = 0.529 A0 = 52.9 pm

• The total energy of the electron in a stationary orbit is equal to sum of its kinetic and potential energies.
• Total energy of electron (E) = K.E. + P.E.
K.E. = 1/2 mv2 = Ze2/2r
P.E. = –Ze2/r

Expression for the energy of Bohrs orbit

• It is important to note that the energy of electron is negative inside the atom.
• As the value of n increases the negative value of energy decreases and the value increases.
• When n is infinity the value of E is zero.
• When an electron jumps from outer energy level (n2) to inner energy level (n1), the energy released

This value is almost equal to Rydberg constant
( R=1,09,677 cm-1).



• The minimum amount of energy required to remove the electron from the outer most energy level of an atom is called its ionization potential.

• The ionization potential of hydrogen atom is 13.6 eV / atom or 2.176 x 10-11 erg / atom or
2.176 x 10-18 J / atom or 1312 kJ/mole or 313.6 kcal / mole.

• When hydrogen gas is heated or exposed to light energy or subjected to electric discharge different atoms absorb different amounts of energy and are excited to different higher energy levels.
• The electrons in the excited atoms maybe completely knocked out of the atom if the absorbed energy is greater than or equal to 13.6 eV which is the ionization potential of hydrogen atom.
• If the energy available is less than 13.6 eV the electron absorbs only a certain quantum of energy which causes electronic transition.
• The electron in higher quantum state tends to emit energy and come back to the lower energy level. This may happen in a single step or in multiple stages.
• When an electron is present in the fourth orbit in the excited state, it may directly come back to the first orbit which gives one line in Lyman series.
• Otherwise the electron may drop from n = 4 to n = 3 and then n= 3 to n = 2 and finally n = 2 to n= 1.
• These transitions result in the formation of one line, each in Paschen series (infrared region) Balmer series (visible region) and Lyman series (ultraviolet region).
• Depending on the type and number of transitions, the electron in the excited state may give number of lines and number of series in atomic spectrum.
• As the value of the principal quantum number increases, the distance between adjacent orbits increases and the energy difference decreases.

• In case of absorption spectrum nf > ni and the term in the parenthesis is positive and energy is observed.

• In case of emission spectrum ni > nf. ΔE is negative and energy is released.
• Orbital frequency = Number of revolutions per second by an electron in a shell

Where E1 = Energy of first shell
• Time period of revolution of electron in nth orbit

The energy required to remove an electron from the ground state to form cation is called ionisation energy.
I.E = E – Eground
= 0 – (–13.6 e.v)
= 13.6 e.v.
= 2.18 x 10-11 ergs
= 2.18 x 10–18 J

Bohr’s model of the hydrogen atom was no doubt an improvement over Rutherford’s nuclear model, as it could account for the stability and line spectra of hydrogen atom and hydrogen like ions (for example, He+, Li2+, Be3+, and so on). However, Bohr’s model was too simple to account for the following points.
• It fails to account for the finer details (doublet, that is two closely spaced lines) of the hydrogen atom spectrum observed by using sophisticated spectroscopic techniques.
• This model is also unable to explain the spectrum of atoms other than hydrogen.
Ex: Helium atom which possesses only two electrons. Further, Bohr’s theory was also unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman effect) or an electric field (Stark effect).
• It could not explain the ability of atoms to form molecules by chemical bonds.
• This theory has limited applications only to one electron systems.
• This theory fails to satisfactorily explain the spectra of multi electron species.
• This gives the possibility of finding the position and velocity of the electron simultaneously.
• But such an experimental determination is impossible due to the wave nature of electron and due to the limited knowledge about the micro particles like electron.

• Interference and diffraction phenomena can be explained with the help of wave nature of light.
• Photoelectric effect and Compton effect can be explained by quantum theory.
• de Broglie proposed that the dual nature is associated with all the particles in motion.
• Electrons, protons, atoms and molecules which are treated as particles are associated with wave nature.
• Einstein’s mass energy equivalence can be mathematically expressed as E = mc2.
• Correlating Planck’s equation and Einstein’s equation.
mc2 = hν

• de Broglie applied this condition for the material particles in motion.
• The wavelength of a particle in motion is inversly proportional to its momentum.
• The wavelength associated with the electron is measurable.
• Hence electron exhibits both wave nature and particle nature.
• de Broglie wavelength of an electron revolving around the nucleus in nth orbit of H – like species is

λ = 3.327 (n/z) A0 = 332.7(n/z) pm

• The wave nature of electron was confirmed by Davison and Germer’s experiment.
• Davison and Germer gave some modified equations for calculation of de Broglie wavelength

Where, q = charge of the particle
m = mass of the particle.
v = accelerating potential

• According to de Broglie, an electron behaves as a standing or stationary wave which extends round the nucleus in a circular orbit.
• If the two ends of the electron wave meet to give a regular series of crests and troughs, the electron wave is said to be in phase.
• In other words there is constructive interference of electron waves and the electron motion has a character, of standing wave or non-energy radiating motion.
• To be an electron wave in phase, the circumference of the Bohr’s orbit should be an integral multiple of the wavelength of the electron wave.

• In case the circumference of the Bohr’s orbit(2πr) is bigger or smaller than nλ, the electron wave is said to be out of phase.
• Then destructive interference of waves occurs causing radiation of energy.
• Such an orbit cannot possibly exist.
• The no. of waves with an electron revolving in nth energy level is equal to ‘n’.

• To locate an electron moving with high velocity it should be illuminated with a beam of light having the wavelength less than the dimension of the electron.
• Radiations having shorter wavelengths than the size of electron consist of high energy photons.
• During the collision with such a high energy photon, the electron gets deflected as it absorbs considerable amount of energy.
• This results in increase in momentum of electron. The change in momentum automatically changes
the position of the electron.
• Thus as we try to observe the electron, its position, speed, path or direction changes.
• Hence it is impossible to determine the exact position and velocity of the electron accurately and simultaneously, If the position is certain velocity is uncertain and vice-versa which is called Heisenberg’s uncertainty principle.

• According to Bohr’s atomic model an electron revolves in certain fixed orbits with a definite velocity.
• This indicates that the position and velocity of an electron are exactly known which is contrary to Heisenberg’s uncertainty principle.
• This principle is mainly applicable for micro scopic particles.

Quantum mechanical model of atom
• Schrodinger’s wave theory is the basis for the modern quantum mechanical model of the atom.
• When the exact position of the electron cannot be determined we can predict the probability of finding the electron around the nucleus.
• This theory takes into account two facts.
1. Wave nature of the electron
2. The knowledge about the position of an electron is based on its probability.
• It describes the electron as a three dimensional wave in the electric field of positively charged nucleus.
• Schrodinger’s wave equation describes the wave motion of electron along x, y and z axes.

• In the above equation ‘m’ is the mass of electron,
E is its total energy, V is its potential energy. is called wave function or amplitude of the electronic wave.
• Acceptable solutions to wave equation are called Eigen wave functions. These are represented by y.
• Solutions to wave equation which are physically possible or meaningful are called acceptable solutions.
• These solutions must satisfy some conditions.
Conditions to be satisfied by acceptable solutions to the wave equation are called “Boundary conditions”.
• They are
1) should be continous.
2) value must be finite.
3) must be single valued.
4) Probability of finding electron over all the space from + to – should be equal to 1.
• The above equation indicates the variation of the value of along x, y and z axes.
2 is the probability function of the electron.
• The region or space around the nucleus where the probability of finding the electron is maximum (about 95%) is called an atomic orbital.
• Wave functions which satisfy the boundary conditions are called Eigen functions.
• Each Eigen function has its specific energy value. These energy values are called Eigen values.
• A set of numbers used to provide a complete description of an electron in an atom are called quantum numbers.
• There are four quantum numbers required for a complete explanation of electrons in an atom.
• The quantum numbers are
a) Principal quantum number
b) Azimuthal quantum number
c) Magnetic quantum number
d) Spin quantum number

• It was proposed by Niels Bohr
• The values of n=1,2,3,4 ….. or K,L,M,N … respectively
• It represents the main energy level or principal energy level.
• It determines the size of the orbit and energy of the orbital.
• The number of sub energy levels in a main energy level is “n”.
• The number of orbitals in a main energy level is “n2”.
• The maximum number of electrons in a main energy level is “2n2”.
• Angular momentum of an electron in an orbit = n(h/2P)


• It is also known as angular momentum quantum number or orbital quantum number (or) subsidary quantum number.
• It is denoted by l and takes values from 0 to n-1.
• When the spectrum obtained using a high resolving spectrometer is observed, more lines are seen.
• Each line in the ordinary spectrum is split into two (duplet), three (triplet) or four (quadruplet).
• This indicates that there are sub energy levels closely bunched together in the main energy level.
• The number of sub levels in a main level is equal to the principal quantum number n.
• The number of sub shells in K shell (n = 1) = 1 (s).
• The number of sub shells in L shell (n = 2) = 2(s,p).
• The number of sub shells in M shell (n = 3) = 3(s, p, d)
• The number of sub shells in N shell (n=4)=4(s, p, d, f)
• Azimuthal quantum number defines the three dimensional shape of the orbital.
• The number of orbitals in a sub shell is (2l + 1)
• The maximum number of electrons in a sub shell is  2(2l + 1).

• To explain Zeeman and Stark effect Lande proposed magnetic quantum number.
• It is denoted by ml.
• It represents the atomic orbital.
• It determines the orientation of orbital in space. The orbit in which the electron revolves resembles a coil in which current is flowing. Hence each orbit is associated with an electric field and as a result a magnetic field is formed in an atom.
• When the atom is placed in an external magnetic field, the orbit changes its orientation.
• The number of orientations is given by the values of the magnetic quantum number m.
• m takes up values from -l to + l total (2l + 1) values.
• A sub shell having azimuthal quantum number l, can have (2l + 1) space orientations.
• If the changes in the axis in one direction are indicated by + m values, the changes in the axis in the opposite direction are indicated by – m .

• In the fine spectrum of alkali metals a pair of widely separated lines are observed which are different from duplet, triplet, and quardruplets observed in the hydrogen spectrum.
• To recognise and identify these pairs of lines Goudsmit and Uhlenbeck proposed that an electron spins about its own axis.
• It is represented by ms and determines the spin of electron
• This results in the electron having spin angular momentum which is also quantised.
• The spinning electron behaves like a magnet.
• In external magnetic field the magnetic moment of an electron can have two space-orientations. One in the direction of external field and the other opposite to it.
• The electron may spin clockwise or anti clockwise correspondingly the spin quantum number takes two values + 1/2 and –1/2
• The formula to caliculate the magnetic movement of an atom or ion

where n = number of unpaired electrons
• An electron has besides charge and mass intrinsic spin agular momentum.
• Spin angular momentum of the electron is a vector quantity.

• The probability of finding the electron in the nucleus is zero.
• The probability of finding the electron in the radial space around the nucIeus is called radial probability.
• The probability function of electron is called D. function.

• The region around the nucleus where the probability of finding an electron is zero called node (or) nodal surface (or) nodal region (or) radial node (or) spherical node.
• The number of nodes (or) radial nodes = n – l -1
• The plane passing through the nucleus where probability of finding an electron is zero called nodal plane (or) planar node (or) angular node.
• The no. of nodal planes are numerically equal to azimuthal quantum number ‘l’.
• The curves are obtained by ploting D function and radial distance (r) are called radial probability distribution curves.

• The shape of s-orbital is spherical and spherically symmetrical. It has no nodal planes. p-orbital has dumb-belI shape. It has one nodal plane.
• The three p-orbitals are mutually perpendicular to one another.
• px orbital is along the x-axis and its nodal plane is along yz plane.
• py orbital is along the y-axis and its nodal plane is along xz plane.
• pz orbital is along the z-axis and its nodal plane is along xy plane.
• px, py and pz differs only in the orientation.
• d-orbital has double dumb-bell shape.
• dxy, dyz, dxz orbitals have 4 lobes in between the axes.
• Each d-orbitals has 2 nodal planes.
• dxy orbital is in the xy plane between x and y axes.
• dyz orbital is in the yz plane between y and z axes.
• dxz orbital is in the xz plane between x and z axes.
• dx2-y2 orbital is also in the xy plane but the lobes are oriented along x and y axes.
• dz2 orbitals is along the z-axis
• dz2 orbital differ from other d-orbitals.
• It also contains a ring called torus or collar or tyre of negative charge surrounding the nucleus in the xy plane.
• Orbitals having same energy are called degenerable orbitals.

Energies of orbitals
• The results obtained by solving the Schrodinger’s wave-equation agree with the experimental values obtained for hydrogen and the other one electron systems like He+, Li 2+.
• The energy of electron in hydrogen atom is determined only by the principle quantum number n.
• In multi electron atoms, the energy level depends on both principal quantum number and azimuthal quantum number.
• 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.
• E2s(H) > E2s(Li) > E2s(Na) > E2s(K)
• The magnetic quantum number m indicates the number of degenerate levels or orbitals of equal energy.
• An orbital having a certain value for m cannot accomodate more than 2 electrons.
• The maximum number of electrons in s, p, d and f sub energy levels is 2, 6, 10 and 14 respectively.

Electronic configuration :
• Filling of electrons in an atom is known as electronic configuration.
• Rules for distribution of electrons in an atom.

• “Electron first enters into orbital having least energy”.
• The energy value of an orbital increases as its (n + l) value increases.
• If two orbitals have the same value for (n + l), the orbital having Iower n value will have low energy.
• upto atomic number 20 the 4s orbital has a lower energy than a 3d orbital.
• As atomic number increases beyond 20, this energy difference between 4s and 3d orbitals decreases and in elements of higer atomic number 4s orbitals has a higher energy than 3d orbital.
• In elements having atomic number greater than 57 , 4f orbitals has lower energy than 5p orbitals.
• Around atomic number 90, energy of 4f orbital is lower than that of even 5s orbital.

• “No two electrons in an atom can have the same set of four quantum numbers”.
• Electrons in the same orbital differ in their spin quantum number and they spin in opposite directions.
• An orbital can not accommodate more than two electrons.

• “When degenerated orbitals are available, pairing of electrons takes place only after all the available orbitals are filled with one electron each” with parallel spin.
• Orbitals having the same values for n and l are called degenerate orbitals.
• Unpaired electrons have parallel spin.
• Half filled and completely filled degenerate orbitals give greater stability to atoms.
• Extra stability half filled and full fill configuration is due to presence of symmetry and exchangable energies.

• Chromium (Z = 24) and copper (Z = 29) have anamolous electronic configuration due to this reason.
• Electronic configuration of chromium atom is
1s2 2s2 2p6 3s2 3p6 4s1 3d5 but not 1s2 2s2 2p6 3s2 3p6 4s2 3d4 .
• Chromium with 3d5 4s1 configuration has 6 unpaired electrons with parellel- spins. Total number of sets of pairs of parallel spins is 15 (2C2)
• In 3d4 4s2 configuration 5 electrons are present with parallel spin. Total number of sets of pairs with parallel spins are 10 (5C2)
• In the configuration 3d5 4s1 the lowering energy is 15K while it is 10 K in the configuration 3d4 4s2. Thus Cr with 3d5 4s1 is more stable than Cr with 3d4 4s2
(k = exchange energy )
• Electronic configuration of copper atom is 1s2 2s2 2p6 3s2 3p6 3d10 4s1 but not is 1s2 2s2 2p6 3s2 3p6 3d9 4s2.



Atomic Structure: Study material for UPSC Civil Services, UGC CSIR JRF NET, NEET, JEE, EAMCET, State Level Eligibility Test and other exams


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