Atomic theories1DEFINITIONFirst Atomic TheoryThe atomic theory of matter was first proposed by John Dalton, known as Dalton's atomic theory.Dalton regarded that atom is the ultimate particleof matter.

2DEFINITIONFundamental Particles

Matter is made up of molecules and moleculesare made up of atoms.Dalton's atomic theory proposed that atoms wereindivisible. But modern discoveries showed thatatom is not indivisible and has a complexstructure.Electrons, protons and neutrons are thefundamental particles of atom.Nucleons:Protons and Neutrons are present in the nucleus and are called Nucleons. Protons are positively charged with unit mass.Neutrons are neutral with unit mass.Electrons:They are negatively charged with negligible mass.3DEFINITIONCathode Ray TubeAtomic structure was obtained from the experimentson electrical discharge through gases. During the discharge tube experiment, Crookesobserved that rays were found to pass from negativelycharged filament (cathode) to positivelycharged plate (anode). 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. By maintaining low pressure and high voltage in discharge tube, current or stream of particles move in the tube from cathode to anode. Those rays are known as cathode rays or cathoderay particles.4DEFINITIONProperties of Cathode RaysCathode rays starts from cathode and move towards anode. These rays themselves are not visible but theirbehaviour can be observed with the help of certainkind of materials (fluorescent or phosphorescent)which glow when hit by them.Rays travel in straight lines in the absence of electricand magnetic field. In the presence of electric and magnetic field, they are deflected whichindicates that cathode rayscontain negatively charged particles known aselectrons.Cathode rays found to be independent of natureof the cathode material and nature of the gas inthe tube.5DEFINITIONCharge to Mass Ratio of an ElectronJ.J.Thomson measured e/m ratio of the electronbased on following points. Greater the magnitude of the charge on the particle, greater is the deflection when electric andmagnetic field is applied. Lighter the mass of the particle, greater will bethe deflection.The deflection of electrons from its original pathincreases when voltage increases from theabove points, Thomson was able to determinethe value of charge to mass ratioas 1.758820 X 1011Ckg16DEFINITIONCharge of an ElectronMullikan determined the charge of the electronby an oil drop experiment By carefully measuring the effects of the electricalfield on the movement of many droplets. Charge on the oildrops was always an integralmultiple of 1.60 X 1019cme=ee/me=1.6010191.7588201011ckg1=9.10941031kg7DEFINITIONProperties of ProtonsAnode rays travel in straight line, and these arematerial particles.Charge:Anode rays are positively charged, and get deflectedby external magnetic field and affect thephotographic plate.emof Anode Rays:emvalue of these rays is smaller than that ofelectrons.emvalue of anode rays depends upon nature ofthe gas.emvalue of anode rays is maximum when thegas present in the tube is hydrogen.Material in Anode Rays:By the dissociation and ionisation of hydrogenunder low pressure discovered with charge +1and mass 1, particles are called proton.8DEFINITIONAtomic ModelsThomson's Model -J.J.Thomson, in 1898, proposed that an atompossesses a spherical shape radius)approximately 1010m) in which the positivecharge is uniformly distributed.According to Thomson, atom is like watermelonand electrons areembeddedlike seeds in watermelon.The positive charge is distributed like fibrousmaterial of water melon. An important feature of this model is that themass of the atom is assumed to be uniformlydistributed over the atom.It cannot explain electrical neutrality of theatom.9DEFINITIONRutherford's Model of an AtomRutherford proposed atomic model based on- ray scattering experiment. Scattering of a narrow beam of- particles asthey passed through a thin gold foil and it is coveredwith fluorescent ZnS screen. When-particles struck the screen, then flash of light wasproduced at that point.

10DEFINITIONObservations of Rutherford's ModelMost of the- particles passes through the foilundeflected.A small fraction of- particles were deflectedby small angles.A very few- particles bounced back were deflectedby 180.11DEFINITIONRutherford conclusions from his experimentRutherford drew the following conclusions from his experiment:

1. Most of the space in the atom is empty.2. A few positively charged alpha particleswere deflected. The deflectionmust be due to enormous repulsive forcesshowing that the positive charge of the atom isnot spread out ofthe atom.3. Main postulates in Rutherfords model. All the positive charge and mass of the atom ispresent in a very small region at the centre ofthe atom. It is called nucleus. The size of the nucleus is very small in comparison to the size of the atom. Most of the space outside the nucleus is empty. The electrons revolve round the nucleus likeplanets revolve round the sun. The centrifugal force arising due to fast movingelectrons balances the coulombic force of attractionof the nucleus and the electrons. Rutherford's atomic model is comparablewith the solar system. So, it is called planetary model.12DIAGRAMDefects of Rutherford's Atomic ModelIt is against the law of electrodynamics.It fails to explain the atomic spectrum orline spectrum.13DEFINITIONAtomic NumberA neutral atom contains equal number ofelectrons and protons. The number of electrons or protons present inan atom of an element is called its atomicnumber. Atomic number is denoted by Z. Atomic number is equal to the nuclear positivecharge of an element.14DEFINITIONMass NumberThe sum of protons and neutrons in the atom ofan element is called its mass number. It is denoted by A. Mass number is always a whole number. Number of neutrons = A -Z15DEFINITIONIsotopesAtoms with identical atomic number but different mass numbers are known as isotopes. Isotopes exhibit similar chemical propertiesEg :Isotopes of hydrogen:Protium(1H1)Deuterium (1H2)orDTritium (1H3)orTIsotopes of chlorine:17Cl35and17Cl37It is evident that difference between the isotopesis due to the presence of different number ofneutrons present in the nucleus.For example, considering of hydrogen atomagain, 99.985% of hydrogen atoms contain onlyone proton. This isotope is calledprotium(11H).Rest of the percentage of hydrogen atom contains two other isotopes, the one containing1 proton and 1 neutron is calleddeuterium(D, 0.015%) and the other one possessing 1 protonand 2 neutrons is calledtritium(T). The latterisotope is found in trace amounts on the earth.Isotopes of an element have the same numberof protons and electrons but differ in the numberof neutrons.16DEFINITIONIsobarsAtoms with same atomic mass number withdifferent atomic number are known as isobars.Eg :146Cl,147N17DEFINITIONWave Length()The distance between twoneighbouring troughs or crests in wave is knownas wave length.The units of wave length are m, cm, A, nm,m.1A=108cm =1010m1nm =1m=10 A2Electromagnetic radiation1DEFINITIONNature of Electromagnetic RadiaitionCosmic rays,- rays, X - rays, UV light,visible light, Infrared light, micro waves, TVwaves and radio waves are calledelectromagneticradiationbecause they are made up ofelectric and magnetic fields propagating in perpendiculardirections in one another. Electromagnetic radiations have wave characteristicsand no medium is required fortheir propagation. They can travel through thevacuum. All electro-magnetic radiations have same velocity.2DEFINITIONFrequency(v)The number of waves thatpass through a given point in one second is calledfrequency.The units of frequency are sec1, cyclesper second (cps) or Hertz (Hz).1 cps = 1 Hz= sec13DEFINITIONWave Number(v)The number of wavelengths per centimeter or the reciprocal of wavelength is called wave number.The unit of wave number is cm1or m14DEFINITIONAmplitude(A)The height of the crest or depthof the trough of a wave is called amplitude. Amplitude is a measure of the intensity orbrightness of a beam of light.5DEFINITIONVelocity(v)The distance travelled by a wavein one second is called its velocity.The units of velocity are m/sec or cm/sec.All types of electromagnetic radiations have thesame velocity which is equal to3x1010cm/ sec or 3x108m/ sec6FORMULARelationship between Wave Characteristicsv=Cor=Cv.......... (1)v=1=vc...........(2)Wherev=frequency in sec1=wavelength in cmC = velocity of light = 3x1010cm/ secv=wave number in cm1The wave length of UV light is 1800 -3800 AThe wave length of visible light is 3800 -7600 AThe wave length of IR radiation is 7600 - 31060 A7DEFINITIONCompton EffectThe increase in wave length or decrease in energyof the X - rays after scattering from an objectis called the Compton effect.8FORMULAPlanck's Quantum TheorySubstances absorb or emit light discontinuouslyin the form of small packets or bundles.The smallest packet of energy is called quantum.The smallest particle of energy is called is called photon.The radiation is propagated in the form of waves.The energy of a quantum is directly proportionalto the frequency of the radiation -EvThe energy of a quantum isE=hv=hc=hcvWhere E = Energy in ergsh =Planck'sconstant = 6.625 x 1027ergsec = 6.625 x 1034JoulesecC = Velocity of light = 3 x1010cm/ sec = 3 x 108m/ secv= Frequency of radiation in sec1=Wave length in cmv=Wave number in cm1A body can absorb or emit in wholenumber of quantum(E=n(hv))9DEFINITIONPhoto-Electric EffectIn 1887, H.Hertz performed a very interestingexperiment that is photo electric effect.E=12375Where E = Energy in eV=wavelength in AThe radiation is propagated in the formof photons. Planck's equation determines both wave natureand particle nature of light.When light is exposed to clean metallic surface,electrons are ejected from the surface. This effectis calledphoto electric effect.The electrons are ejected from the metal surfaceas soon as the beam of light strikes the surface,i.e., there is no time lag between the striking oflight beam and the ejection of electrons.Conditions for Photo-electric Effect:.Ejection of electrons from the surface of a metalby irradiating it with light of suitable frequency.The photo electric effect is readily exhibited byalkali metals like K and Cs.A part of the energy of photon is used to escape the electron from the attractive forcesand the remaining energy is used in increasing the kinetic energy of electron.hv=W+KEK.E.=12meV2 ,W=hvohv=hvo+12meV2me=mass of the electron, V = velocity of theejected electron,vo=Threshold frequencyEffect of Intensity and Frequency of Light:In photo electric effect, the number of photo electronsemitted is proportional to intensity of incidentlight.Kinetic energy of photo electrons depends onlyon the frequency of incident light and not on theintensity of light.The minimum energy required for emission ofphoto electrons is called threshold energy or workfunction.For each metal, there is a characteristic minimumfrequencyvo(also known asthreshold frequency)below which photoelectric effect is not observed.At a frequencyv>vothen photoelectric effectis observed.3Bohr's atomic model1DEFINITIONSpectraSpectrum formed by rays and its properties:

1. Sun light or light from an incandescent filamentlamp gives a continuous spectrum.2. When a gas or a vapour of a metal is kept in adischarge tube and higher potential is applied, aline spectrum is formed.3. Each element has its own characteristic linespectrum.4. The characteristic lines in atomic spectra can beused in chemical analysis to identify unknownatoms in the same way as finger prints are usedto identify people.5. The spectra obtained by the emission of energy by the excited atoms are calledemission spectra.6. These spectra consist of bright lines on the darkbackground.7. When white light is passed through a gas andthe emergent beam of light is allowed to fall on aphotographic plate, the spectrum obtained iscalledabsorption spectrum.8. As the substance absorbs certain portion of whitelight, dark lines appear on bright background.9. For a given element, dark lines in the absorptionspectrum coincides with the bright lines in theemission spectrum.10. An absorption spectrum is like the photographicnegative of an emission spectrum.11. German chemist, Robert Bunsen(1811-1899) wasone of the first investigators to use line spectrato identify elements.2DEFINITIONHydrogen SpectraThe source of radiation here is a hydrogendischarge tube. The discharge tube contains hydrogen gas at lowpressure and high potential difference. The bright light emitted from the discharge tubeis passed through a prism to cause dispersion. The emergent beam of light falls on aphotographic plate and is recorded as the atomicspectrum of hydrogen. The hydrogen spectrum is the simplest of all theatomic 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 eyeand is termed as the visible region of hydrogenspectrum. As it was discovered by Balmer, it is calledBalmerseries.3DEFINITIONBalmer SeriesThe wavelength or wave number of various linesin the visible region can be expressed by anequation.v=1=R[1n211n22]wheren1= 2 which is constant for all the lines inBalmer series.n2= 3, 4, 5......R is Rydberg constant and its value for hydrogenis 1,09,677 cm1(or)1.09677 x 105cm1Ryedberg constant value is not same for all theelements.The first line in Balmer series is called Hlineand its wavelength is 6563 A. The second line is called Hline and itswavelength is 4861 AThe spectral lines get closer when the n2value isincreased.If n2is taken as infinity the wavelength of thelimiting line in the seriesis obtained.v=1=R[12212]=R4= 27,419 cm1The other series in the hydrogen spectrum areinvisible.The wavelength or wave numbers of all the linesin all the series can be calculated by usingRydberg's equationv=1= 1,09,678(1n211n22)Maximum number of lines produced whenan electron jumps from nth level to groundlevel=n(n1)24DEFINITIONSeries of Hydrogen Spectrum

The value of R = 1,09,678 cm1is valid only forthe lines in the hydrogen spectrum.For a spectral line of any one electron specieslike He+, Li2+the value ofR=RHZ25DEFINITIONPostulates of Bohr's ModelEnergy Levels:The electrons in an atom revolve around the nucleus in definite circular orbits or shells or energylevels.Stationary States:So far an electron revolves in a certain orbit,its energy remains constant and does not radiateenergy. These orbits are called stationary orbitsor stationary states.Angular Momentum of Electron in an Orbit:Electrons can revolve only in those stationaryorbits in which their angular momentum is equalto integral multiple ofh2mvr=nh2where m = mass of electron v = velocity of electron, r = radius of orbit n = 1 , 2 , 3 ,4 ...... h = Planck's constantJust as linear momentum is the product ofmass (m) and linear velocity (v), angularmomentum is the product of moment of inertia (I)and angular velocity (). For an electron of massm, moving in a circular path of radius r aroundthe nucleus, angular momentum =ISinceI=mer2, and=v/rwhere v is thelinear velocity,angular momentum =mr2v/r=mvrDifference in Energy Levels:When an electron drops from a higher orbit toa lower orbit, energy is released. When an electronjumps from a lower orbit to a higher orbit,energy is absorbed. The absorbed or evolvedenergy is equal to the difference in energies oftwo orbits, which is equal to quanta.E=E2-E1=hvThe line spectrum is obtained due to the electronictransition from one orbit to another orbit.Force of Attraction:The force of attraction between the nucleus andthe electron =Ze2r2The centrifugal force of the electron due to revolving around the nucleus =mV2r6DEFINITIONRadius of Bohr's OrbitExpression for the radius of Bohr's orbitr=n2h24mZe2where r = radius of orbit n = 1, 2, 3, 4 ...... h = Planck's constant m = mass of electron Z = atomic number e = charge of electronRadius of Hydrogen atom,r=0.529 x108xn2cm =0.529 xn2ARadius of orbits in H atom like ionsr=0.529n2ZA7FORMULAVelocity of an Electron in Hydrogen AtomVelocity of electron in hydrogen atomV=2Ze2nh=2.188108ncm/secwhere V = velocity of electron e = charge of electron n = 1, 2, 3, 4 ....... h = Planck's constantFor hydrogen atom,Vn=V1nwhereVn=Velocity of electron in nth orbit V1=Velocity of electron in first orbit n = 1, 2, 3, 4 ........For H atom like ions.Vn=ZV1nwhereVn= Velocity of electron in nth orbit V1= Velocity of electron in first orbitof H-atom n = 1, 2, 3, 4 ....... Z = Atomic number8FORMULAEnergy in Bohr's orbitKinetic energy of electron =12mV2=Ze22rPotential energy of electron =Ze2rTotal energy of electron=KE+PE=Ze22rZe2r=Ze22rExpression for the energy of Bohr's orbitE=22mZ2e4n2h2where E = energy of orbit m = mass of electron e = charge of electron n = 1, 2, 3, 4 ........ h = Planks constantEffect of Kinetic,Potential and Total Energies asnIncreases:As we go to higher orbits, kinetic energydecreases, potential energy increases andthe total energy increases.Energy of orbits in hydrogen atom ( Z = 1 )Energy Expressions in Different Units:E=2.1791011n2ergs =2.1791018n2joules =13.6n2eV =313.6n2Kcal/mole =1312.6n2KJ/mole1eV=1.6021019JThe energy of the electron in a hydrogen atomhas a negative sign for all possible otbitalsbecause the energy of the electrons in the atomis lower than the energy of a free electron at rest.Energy of orbits in H atom like ionsE=2.1791011n2Z2ergsEn=E1n2whereEn= Energy of nth orbit in hydrogen atomE1= Energy of first orbit in hydrogen atomn = 1, 2, 3, 4 .........For Hydrogen atom like ions.En=Z2n2E1whereEn= Energy of nth orbit in other ions likeH - atomZ = Atomic numbern = 1, 2, 3, 4 ........E1= Energy of first orbit in hydrogen atomIonisation of Electron:Ionisation Potential is the energy required for removal of electron from the outermost orbit.For hydrogen atom, Ionizationpotential =E1n2For H atom, like ions, Ionisationpotential =E1Z2n2Ionisation potential of an atom orion =13.6[Z2n2]eV9DEFINITIONRydbergs constantR=22mZ2e4h3C=109680cm1Difference of energy between two Bohr orbits ofhydrogen atomE=Rhc[1n211n22]whereE= Energy difference R = Rydberg constant h = Planck's constant c = Velocity of light n1= lower orbit, n2= higher orbitAs the value of n increases, the difference ofenergy becomes smaller. After a certain stage, the energy becomes nearly equal and this positionof continuum is calledcritical energy. If energyis slightly greater than this given value, thenthe electron will be completely removed from theatom.Difference of energy between two orbits in H atomlike ions.E=Z2Rhc[1n211n22]where Z = atomic number.

10DEFINITIONMerits of Bohrs modelIt successfully explains the hydrogen spectrumand spectra of ions having one electron.The experimental values of the energies andradii of possible orbits in hydrogen atom are ingood agreement with that calculated on the basisof Bohr's theory.The experimental value of Rydberg constant forhydrogen is in good agreement with that calculatedfrom Bohr's theory.The calculated value ofionizationenergy of hydrogenusing Bohr's theory is very close to the experimental value.11DEFINITIONLimitations of Bohr's Model1. It failed to explain the spectra of atoms or ionshaving more than one electron.The fine structure of spectral lines cannot beexplained by Bohr's theory.2. It failed to explain Zeeman effect and Stark effect.3. Bohr model of the hydrogen atom, not onlyignores dual behavior of matter but alsocontradicts Heisenberg uncertainty principle.Zeeman Effect:The splitting of spectral lines of an atom into agroup of fine lines under the influence of amagnetic field is called Zeeman effect.Stark Effect:The splitting of spectral lines of an atom into groupof fine lines under the influence of an electric fieldis called Stark effect.4de-Broglie's hypothesis1DEFINITIONde-Broglie Wave Theory:The wave nature of electron was first proposedby de Broglie.According to de Broglie theory, all moving particleshave wave properties.Wave properties are important only for particlesof small mass and high velocity.de Broglie equation is=hmv=hpwhere=wave length h = Planck's constant = 6.625 x1034J.sec v= Velocity of the particle m = mass of the particle p = Momentum of the particle

According to de Broglie's theory, electrons revolvearound the nucleus in atomic orbits withstationary waves.Electrons revolve in those orbits, whose circumferencemust be equal to integral multiple ofwave length2r=nwhere r = radius of the orbit n = 1, 2, 3, 4 ..... = wavelengthNumber of waves in an orbit = nNumber of revolutions of an electron persecond in an orbit =Velocityofelectroncircumference2DEFINITIONBohr's Theory and de-Broglie's ConceptAccording to de Broglie, an electron behaves asa standing or stationary wave which extends aroundthe nucleus in a circular orbit.If the two ends of the electron wave meet to givea series of crests and troughs, the electron waveis said to be in phase. In other words, there is constructive interferenceof electron waves and the electron motion has acharacter of standing wave or non-energy radiatingmotion.To be an electron wave in phase, thecircumference of the Bohr's orbit should be anintegral multiple of the wavelength of the electronwave.n=2r

Explanation of de Broglie's Concept:In case, the circumference of the Bohr's orbit(2r)is bigger or smaller thann, the electronwave is said to be out of phase.Then, destructive interference of waves occurscausing radiation of energy.Such an orbit cannot possibly exist.The wavelengths associated with ordinary objectsare so short (because of their large masses) thattheir wave properties cannot be detected.5Heisenberg's uncertainty principle1DEFINITIONHeisenberg's Uncertainty PrincipleIt is impossible to determine accurately and simultaneouslythe position and momentum of aparticle in an atom. It is calledHeisenberg's uncertainty principle.The uncertainty principle equation isx .ph4x . mvh4wherex= uncertainty in position p= uncertainty in momentum v= uncertainty in velocity m = mass of the particle h = Planck's constantThe uncertainty principle is mainly applicable formicroscopic particles.

Explanation for Heisenberg's Uncertainty Principle:To observe an electron we can illuminate it withlight or electromagnetic radiation. The lightused must have a wavelength smaller than thedimesions of an electron. The high momentumphotons of such light(p=h)would changethe energy of electrons by collisions. In thisprocess we, no doubt, would be able to calculatethe position of the electron, but we would knowvery little about the velocity of the electron afterthe collision.If one of tries to find the exact location of theelectron, say to an uncertainty of only 108m,then the uncertaintyvin velocity would be104m2s1108m10+4ms1which is so large that the classical picture ofelectrons moving in Bohr's orbit (fixed) cannothold good.6Orbitals and Quantum numbers1DEFINITIONRadial Probabilty DistributionThe probability of finding an electron at a certaindistance from the nucleus is calledradialprobability.The curves obtained by plotting probability functionD=4r2dr2and radial distance (r) arecalledradial probability distribution curves.Number of peaks obtained in a curve = n - lwhere n = principal quantum number l = Azimuthal quantum number

The nodal surface of 2s orbital exists at a distanceof 2aofrom the nucleus. Where aois theBohr radius 0.529 AThe curve for 2s orbital has two peaks, the curvepasses through lower maximum at 0.53 Aandhigher maximum at 2.6 Aradial distance.2DEFINITIONOrbitalsThe space around the nucleus of an atom in which there is a maximum probability of finding an electron is called an orbital.The maximum probability of finding an electron in an orbital is 95 %.The plane where the probability of finding the electrons is zero(2=0)is called a nodal plane.Number of nodal planes in an orbital = l.3DEFINITIONs orbitalThe shape of s orbital ( l = 0 ) is spherical.s - orbital is a non directional orbital.4DEFINITIONp orbitalIn a p - sub shell, the three orbitals are represented as px, py, and pz. These are degenerate orbitals.The shape of a p - orbital ( l = 1 ) is dumbbell.p - orbitals are oriented along the axes. So they are directional orbitals.Orbital : pxpy pzm :1 1 05DEFINITIONd orbitalIn a d - sub shell, the five orbitals are represented as dxy, dyz, dzx,d{x2y2}and d2z.These are degenerate orbitals.The shape of a d - orbital ( l = 2 ) is double dumbbell.dxy, dyzand dzxorbitals are oriented in between the axes dx2y2and d2z orbitals are oriented along the axes.Orbital : dxy dyz dzx dx2y2 d2zm :2 1 1 2 06DEFINITIONNo. of nodal planes

When the number of nodal planes increases, theenergy of the orbital increases.So the energyorder of the orbitals is s < p < d < fNumber of radial nodes =nl1wheren=principal quantum number l= Azimuthal quantum number7DEFINITIONQuantum NumbersA set of numbers used to provide a complete description of an electron in an atomare called quantum numbers.There are four quantum numbers requiredfor a complete explanation of electrons inan atom.The quantum numbers aren-Principal quantum numberl-Azimuthal quantum numberm- Magnetic quantum numbers-Spin quantum number8DEFINITIONPrinciple Quantum Number(n)It was proposed by Niels Bohr.Possible Values of Principle Quantum Number:The values of n =1, 2, 3, 4 ..... or K, L,M, N ....... respectively.It indicates the size and energy of theorbit.The maximum number of electrons in anorbit = 2n2Total number of orbitals = n2where n = no.of the orbitAngular momentum of an electron in anorbit =nh2

9DEFINITIONAzimuthal Quantum Number(l)It was proposed by Sommerfield.Possible Values of Azimuthal Quantum Number:The values ofl= 0, 1, 2, .....( n -1 ).The values oflrepresents various sub shells. Whenl= 0, 1, 2, 3 ...... etc are calleds, p, d, f ....... sub shells respectively.Energies are in the order ofs < p < d < f .It indicates the shape of orbit or orbitaland angular momentum of electron.Number of sub shells in an energylevel = nwhere n = no.of the orbitAngular momentum of the electron in anorbital =h2l(l+1)=hl(l+1)(h=h2)whereh= Planck's constant l= Azimuthal quantum number10DEFINITIONMagnetic Quantum Number (m)It was proposed by Lande.Possible Values of Magnetic Quantum Number:The values of m = +l..... 0 ..... -l.The total m values = 2l+ 1The total number of m values indicates the total number of orbitals in the subshell.The number of orbitals in s, p,d and f sub shells are 1, 3, 5 and 7 respectively.It indicates the orientation of orbitals in space.The number of orbitals in an energy level n2The number of orbitals in a sub shell = 2l+1Maximum number of electrons in a subshell 2(2l+ l)wherel= Azimuthal quantum number.11DEFINITIONSpin Quantum Number (s)It was proposed by Goudsmit and Uhlenbeck.Possible Value of Spin Quantum Number:The values ofs =+12and12The clock wise direction spin is representedby+12and anticlock wise direction spin is representedby12For each value of m, there can be two values.It indicates the direction of the spin ofthe electron.Maximum number of electrons in anorbital = 2.The maximum number of electronspresent in s, p, d and f shells are 2, 6, 10and 14 respectively.

7Important Principles1DEFINITIONPauli's Exclusion PrincipleNo two electrons in the same atom can have thesame values for all the four quantum numbers.

Two electrons in a given orbital have same valuesof n, l and m.Electrons in the same orbital differ in their spinquantum number and they spin in oppositedirections.

Consequence of Pauli's Exclusion Principle:An orbital can not accommodate morethan two electrons.2DEFINITIONAufbau PrincipleElectron filling follows energy ranking.The orbitals are successively filled in the order oftheir increasing energy.Among the available orbitals, the orbitals of lowestenergy are filled first.

Energy of the Orbital in terms ofn+l:The energy value of an orbital increases as its(n+l) value increases.If two orbitals have the same value for (n+l), theorbital having lower n value is first filled.3DEFINITIONHund's RuleOrbitals of the same kind should be half filledbefore electron pairing takes place.

Degenerate Orbitals:Orbitals having the same values for n and l arecalled degenerate orbitals.Unpaired electrons have parallel spin.Half filled and completely filled degenerate orbitalsgive greater stability to atoms.

Example:Chromium (Z = 24) and copper (Z = 29) haveanomalous electronic configuration due to thisreason.Electronic configuration of chromium atom is1s22s22p63s23p63d54s1but not 1s22s22p63s23p63d44s2.4DEFINITIONStability of Completely Filled and Half Filled Sub-ShellsThe valence electronic configurations of Cr andCu are 3d54s1and 3d104s1respectively and not 3d44s2and 3d94s2.

Reasons:The completely filled and completely half filled sub-shells are stable due to the following reasons.

Symmetrical distribution of electrons:It is well known that symmetry leads to stability. The completely filled or half filled subshells have symmetrical distribution of electrons in them and are therefore more stable.

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.