1. ATOMIC STRUCTURE. Specific Charge (e/m) c/g

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1 1. ATOMIC STRUCTURE Synopsis : Fundamental particles: According to Dalton atom is te smallest indivisible particle. But discarge tube experiments ave proved tat atom consists of some more smaller particles. Electrons, protons and neutrons are te fundamental particles of an atom. Electron was discovered in catode ray experiment. Ideal conditions to produce catode rays in te discarge tube are very low pressure (0.01 mmhg) and ig electric discarge (10,000 V) potential. Catode rays can be deflected in electric and magnetic field wic sows tat tey are negatively carged particles. Particle nature of catode rays was proved by (a) Teir ability to cause mecanical motion (b) Poto-electric effect (c) Compton effect. Catode rays are negatively carged consisting of electrons. Anode rays are positively carged ions. Protons and neutrons are present in te nucleus and are called as nucleons. Protium contains only electron and proton. Except protium all te atoms contain electron, proton and neutron. Electrons are te negatively carged particles wit unit negative carge and negligible mass. Protons are te positively carged particles wit unit mass. Proton was discovered in te anode ray experiment. Anode rays, also called as canal rays or positive rays, were discovered by E. Goldstein. Anode rays contain material particles obtained by te removal of one or more electrons from te gaseous atoms/ molecules present in te tube. Te positively carged particles present in te anode rays produced wen Hydrogen gas is present in te discarge tube were called protons by Ruterford (proton = first particle). Te specific carge on te anode rays was found to be maximum wen gas present in te discarge tube was ydrogen. Neutrons are neutral particles wit unit mass Fundamental Carge particle Electron coulomb (or) e.s.u. Proton Neutron coulomb (or) e.s.u. 0 Mass kg (or) a.m.u. 1/1836 of H atom kg (or) a.m.u kg (or) a.m.u. Specific Carge (e/m) c/g c/g 0 1

2 Te ratio of carge to mass is called specific carge. Electron as te igest specific carge because of its negligible mass. Te mass of electron increases wit increase in velocity. Tus e/m of electron decreases wit increase in velocity. If electron moves wit a velocity equal to tat of ligt, ten it's mass becomes infinity and e/m becomes zero. e/m of catode rays is independent of nature of te gas in te discarge tube, because electrons are universal constituents. e/m of anode rays depends on te nature of te gas in te discarge tube. Te number of electrons or protons present in an atom of an element is called its atomic number. A neutral atom contains equal number of electrons and protons. Atomic number is denoted by Z. Atomic number is equal to te nuclear carge of an element. Moseley proposed a simple relationsip between frequencies of te caracteristic x-rays of an element and its atomic number. υ = a(z b) υ is te frequency of caracteristic x-rays. Z = atomic number 'a' and 'b' are constants aving definite values for tat element. Te sum of number of protons and neutrons in te atom of an element is called its mass number and it is denoted by 'A' Number of neutrons = A Z. Mass number is always a wole number. Atoms of elements aving te same atomic number but different mass numbers are called isotopes. Isotopes of an element ave te same number of protons and electrons but differ in te number of neutrons. Isotopes of an element ave same cemical properties but different pysical properties. Ruterford's atomic model: Tis is called planetary model or nuclear model of atom. Ruterford's atomic model is based on te findings of α-ray scattering experiment. An atom is a ollow spere and te entire mass and positive carge are concentrated at te centre of te atom in te smallest region called nucleus. Electrons revolve around te nucleus in circular pat. Tis model failed to explain te stability of atoms and line spectra of atoms. As per te laws of electrodynamics an electron moving around te nucleus must radiate energy continuously and must spiral down into te nucleus. If an electron radiates energy continuously te atomic spectrum sould be a continuous spectrum. Te atom sould collapse if it appens. But all te atoms give line spectra. Nature of ligt: Te two teories, wic explain te nature of ligt are (i) wave teory, (ii) corpuscular teory. Te wave teory of ligt could satisfactorily explain diffraction, refraction etc.

3 3 Corpuscular teory could explain potoelectric effect and Compton effects. Wave teory is superior to corpuscular teory. Visible ligt is only a small portion of electromagnetic spectrum. All radiant energy is in te form of electromagnetic waves. Tese radiations are associated wit electric and magnetic fields. Te vertical component of te wave (E) indicates te variation of electric field strengt. Te orizontal component of te wave (H) indicates te variation of magnetic field strengt. Te distance between two successive crests or trougs is called te wavelengt (λ). Wavelengt is measured in Angstrom units or nanometres. 1 Å = 10 8 cm = m; 1 nm = 10 9 m = 10 Å Te number of waves passing troug a given point in one second is called as frequency of te wave. υ = c / λ Units of frequency is Hz. Te velocity of ligt in air or in vacuum is 10 8 ms 1 or cms 1. Frequency wavelengt = velocity; υλ = c Te reciprocal of wavelengt is called wave number. 1 Wave number υ = λ Te units of wave number is cm 1 or m 1. 1 υ = λ υ = c ; λ ; υ = c. υ 'A' is te amplitude of te wave or intensity of te ligt. Te intensity of color depends on amplitude and color of te ligt depends on frequency. (I A ) Sources of different radiations: Hig-pressure ydrogen or deuterium discarge tube is te source of ultraviolet rays. Te wavelengt range of ultraviolet rays is 1850 Å to 3750 Å. To obtain ig energetic U.V. xenon arc lamp or mercury vapour lamp can be used. Te glass enclosed tungsten filament is te source of visible radiation. Incandescent lamp is te source of I.R. radiation. Te best source of near infrared radiations is a black body. To produce far infrared radiations Nernst glower or globar source is used. Te wavelengt of tese radiations is about 14,000 Å. A mixture of Zirconium and Yttrium oxides saped into a small ollow rod is used in Nernst glower. Te glower is eated to 1500 C to 000 C. Te globar source is a rod of sintered silicon carbide, wic is eated to 1300 C to 1700 C. Planck's Quantum teory: Planck's quantum teory explains black body radiation. A ollow spere coated inside wit platinum black and aving a pinole acts as a nearer black body.

4 4 A black body is not only a prefect absorber but also a perfect emitter of radiant energy. Black body kept at ig temperature give radiations in a wide range of different wavelengts. Te curves are obtained at different temperatures wen te intensity of radiations is plotted against wavelengt. If te energy is emitted continuously te curve sould be as sown by te dotted lines. Te study of te curves sows tat te nature of te radiation depends on temperature. At a given temperature, te intensity of radiation increases wit wavelengt reaces a maximum and ten decrease. As te temperature increases te peak of te curve sifts to lower wavelengts. (ie. towards left) Based on te above observations of black body radiation, Planck proposed quantum teory of radiation. Te salient features of te teory are Te vibrating particle in te black body does not emit energy continuously. It is emitted in te form of small discrete packets called quanta. Te emitted radiant energy is propagated in te form of waves. If te vibrating particles oscillates wit a frequency v, ten te energy associated wit a quantum. E v; E = v ( = Planck's constant. = ergs-sec, = 6.65 X J-sec) Energy is emitted or absorbed in some simple integral multiples of a quantum i.e. E = 1 v (or) v (or) 3v but not fractional multiple of v. Tis is called quantization of energy. Einstein's generalisation of Planck's quantum teory: Planck's quantum teory was extended to all types of electromagnetic radiations by Einstein. According to Einstein energy is released in te form of potons and tey continue to exist as potons till tey are absorbed by anoter body. According to Max Planck, energy is emitted in te form of packets and propagated in te form of waves. According to Einstein, bot emission and propa-gation of energy take place in te form of potons. Einstein explained potoelectric effect wit te elp of is generalized quantum teory. Emission of electrons from te metal surface wen it is exposed to ligt is called potoelectric effect. Suc emitted electrons are called potoelectrons. According to Einstein electron is ejected from a metal wen it is struck by a poton wic as sufficient energy. If te poton as insufficient energy it cannot eject te electron and poto electric effect is not observed. Poton of violet ligt as iger energy tan tat of red ligt. It is observed tat violet ligt is able to eject electrons from potassium but red ligt as no effect. Wen te poton aving energy v, strikes te metal surface, some part of it is utilised to eject electron and te remaining part is utilised to increase te K.E. of poto electron. If te frequency of incident radiation increased, K.E. of potoelectrons increase. If te intensity of incident radiation increases rate of potoelectric emission increases. v = W + K.E v = energy of striking poton; W = energy required to eject te electron (work function); K.E. = kinetic energy of te emitted electron.

5 Ligt spectra: Spectrum: It is te pattern of lines produced on te potograpic plate, by te dispersion of a beam wen it is passed troug te prism. Spectrometer: It is te device used to record te spectrum. Spectrograp It consists of source of ligt, Prism and potograpic plate. Spectra are of types: 1. Emission spectrum. Absorption spectrum Emission Spectrum: Wen te substances are in te excited state tey emit ligt. Spectrum obtained wit tis emitted ligt is called emission spectrum. Emission spectrum is obtained by eating te substances on a flame or by passing electric discarge troug te gases. Emission spectrum consists of brigt lines on dark background. Absorption spectrum: It is due to absorption of ligt. Wen te substances are in te ground state, tey absorb radiation and go to excited state, te spectrum so obtained is called absorption spectrum. Absorption spectrum consists of dark lines on brigt background. In te absorption spectrum lines are formed at same wavelengts as tose of emission spectrum. Emission spectrum or absorption spectrum is of two types. Continuous spectrum or band spectrum: In tis spectrum formation of lines is continuous. Eac color fades in to te next color as in rainbow. A beam of wite ligt wen passed troug a prism, it gives a continuous spectrum of seven colors i.e. VIBGYOR. Incandescent lamp or ot solids at ig temperatures will give continuous spectrum. Discontinuous spectrum or line spectrum: Line spectrum consists of sarp, distinct and well defined lines. Gases or vapours of elements wen eated in a flame or by passing electric discarge troug tem, line spectrum is obtained. Line spectrum is given by atoms and so it is called atomic spectrum. Eac element as it's own caracteristic line spectrum, by wic te element can be identified. Band spectrum: It consists of series of bands were eac band is a group of lines merged togeter. Band spectrum is given by molecules and so it is called molecular spectrum. Hydrogen spectrum: It consists of number of lines. Tey can be classified into various series. Only one suc series is visible to te naked eye and is termed as te visible region of ydrogen spectrum i.e. Balmer series. Te wavelengt or wave number of various lines in te visible region can be expressed by an equation. (Reydberg Ritz equation ) : 5

6 1 υ = = R λ n n 1 Were n 1 = wic is constant for all te lines in Balmer series; n = 3, 4, 5... Series in ydrogen spectrum: Name of series n 1 (lower orbit) n (iger orbit) Spectral region Lyman series 1, 3, 4, 5... ultraviolet Balmer series 3,4,5,6... visible Pascen series 3 4,5,6,7... near infrared Brackett series 4 5,6,7... infrared Pfund series 5 6,7,8... far infrared Te oter series in te ydrogen spectrum are invisible. Te wavelengt or wavenumber of all te lines in all te series can be calculated by using Rydberg's equation or Rydberg-Ritz equation. 1 υ = = R λ n n 1 Te value of R = 1,09,677 cm 1 is valid only for te lines in te ydrogen spectrum. For a spectral line of one electron species like He +, Li + te value of R = 1,09,677 Z cm 1. Te first line in Balmer series is called Hα line and its wavelengt is 6563 Å. Te second line is called Hβ line and its wavelengt is 4861 Å. Te spectral lines get closer wen te n value is increased. Bor's atomic teory: Bor recognized te relationsip between te nature of te series of spectral lines and te arrangement of electrons in te atom. Bor applied Planck's quantum teory to te electrons revolve around te nucleus. He retained te basic concept of Ruterford's model of atom tat electrons revolve round te positively carged nucleus. Bor proposed is teory to explain te structure of atom. Te important postulates of is teory are: Electrons revolve around te nucleus wit definite velocities in concentric circular orbits. Tese orbits are called stationary orbits as te energy of te electron remains constant. As long as te electron revolves in te same circular orbit it neiter radiates nor absorbs energy. Te angular momentum of te electron is quantised. Te electronic motion is restricted to tose orbits were te angular momentum of an electron is an integral multiple of /π or mvr = n/π. Tis is called Bor's quantum condition or quantisation of angular momentum. Energy of te electron canges only wen it moves from one orbit to anoter orbit. Energy is absorbed wen an electron jumps from a lower orbit to a iger outer orbit. If electron is in 1s orbit, it can only absorb but cannot emit energy. Energy is released wen an electron jumps from iger orbit to a lower orbit. 6

7 Te released or absorbed energy is equal to te difference between te energies of te two orbits. If E is te energy of te electron in te outer orbit (n ) and E 1 is te energy of te electron in te inner orbit (n 1 ), ten E E 1 = ΔE = υ. Were n is called principal quantum number and it represents te main energy level. It takes all positive and integral values 1,, 3, 4 etc. Wit te elp of tese postulates Bor derived te expression for te radius of te circular orbit, energy of te electron in a circular orbit and velocity of te electron in a circular orbit. Bor's teory could satisfactorily explain te formation of different series of lines in ydrogen spectrum. Te wavelengts and te frequencies of te lines determined experimentally are in excellent agreement wit tose calculated by using Bor's equation. Radius of orbit: Hydrogen atom contains one proton in te nucleus and one electron revolving around te nucleus in a circular orbit of radius r. Te electron maintains te same circular motion in given orbit as centripetal and centrifugal forces are equal in magnitude and opposite in direction. Centripetal force = centrifugal force (columbic forces of attraction provides necessary centripetal force) e mv = e = mv i.e. r r r According to Bor's quantum condition; n n mvr = v = π ; πmr ; n e m n n n v = = e = r = 4π m r r ; 4π m r ; 4π mr ; 4π me Te radius of te nt orbit is given by r n = n 4π me = n cm Were = Planck's constant; m = mass of electron; e = carge of electron; r n = radius of nt orbit Te radius of te first orbit of ydrogen atom is called Bor's radius wic is denoted by r 0. r 0 = cm = 0.59 Å Energy of electron: Te total energy of te 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. is always positive and P.E is always negative. K.E. is alf to tat of P.E. in magnitude. 1 e 1 e e e 1 e mv = ( mv = ) = r r r r r 4 π e m z x Energy of electron for single electron species is E n = n. 7

8 By substituting te value of r. 1 e 4π me E n = n E n = 4 π e m n k E n = n (k is constant ; k = 13.6 E n = n ev/atom (or) (or) ; 11.18x10 n 18.18x10 n n ; ergs/atom J/atom 4 π e m ); (or) kcal/mole 131 n kj/mole Te energy of electron is negative in te atom. As te value of n increases energy increases. Wen n is infinity te value of E is zero. Wen n value decreases te energy of electron also decreases. Rydberg constant (R): Wen an electron jumps from outer energy level (n ) to inner energy level (n 1 ), energy is released. i.e. E E 1 = ΔE = Δυ E = energy of electron in iger orbit (n ) E 1 = energy of electron in lower orbit (n 1 ) 4 4 π e m π e m + n E E 1 = n1 ; 4 π e m ΔE = n n 1 ; 4 π e m υ = n n 1 ; 4 π e m 3 υ = n n 1 ; 1 v υ = = Wave number λ c 8

9 9 4 4 π e m υ = π e m c υ = 3 3 υ = c υ ; n1 n c ; n1 n ; 1 υ = = R λ n1 n 4 π e m 3 R = c = 1,09,681 cm 1. Tis value Rydberg constant (R) calculated by Bor as above is in good agreement wit experimental value. Velocity of element in te nt orbit: n As per Bor s quantum condition, mvr = n π πmr ; V n = ; πe πe z x Substituting r ; V n = n (for H atoms for any oter single electron species; V n = n Sub situating te values of constants,.188 z x 8 V n = 10 n cm/sec. velocity v = Number of revolutions per second, made by electron in circular orbit is = circumference πr Hydrogen spectrum Bor s explanation: Wen ydrogen gas is eated or exposed to ligt energy or subjected to electric discarge different atoms absorb different amounts of energy and electrons are excited to different iger energy levels. Te brigt ligt emitted wen passed troug a prism and received on a potograpic plate and is recorded as te atomic spectrum of ydrogen. Te ydrogen spectrum is te simplest of all te atomic spectra. It is line spectrum and emission spectrum. It contains a number of series of lines. Te electrons in te excited atoms may be completely knocked out of te atom if te absorbed energy is greater tan or equal to ev wic is te ionization potential of ydrogen atom. If te energy available is less tan ev te electron absorbs only a certain quantum of energy and te electron jumps to iger orbit. Te electron in iger quantum state tends to emit energy and come back to te lower energy level. Tis may appen in a single step or in multiple steps. If electron jumps from any iger orbit to 1 st orbit Lyman series is formed in u.v. region. Electron transitions: so on. If electron jumps back from any iger orbit to nd orbit Balmer series is formed in visible region. Electron transitions: ; 7, 6 If electron jumps back from any iger orbit to 3rd orbit Pascen series is formed in near I.R.

10 10 region. Electron transitions: 3; 7 3, 6 3; and so on. If electron jumps back from any iger orbit to 4 t orbit, Bracket series is formed in te I.R. region. Electron transitions: 4; 7 4, 6 4 and so on. If electron jumps back from any iger orbit to 5 t orbit. Electron transitions: 5; 7 5, 6 5 If electron jumps back from infinite state to corresponding lower orbit, spectral line is called limiting line or limiting series R v = R = n n Rydberg's equation for limiting line is 1 1 n a given series te line of longest wavelengt is 1 st line ( 1) and te line of sortest wavelengt is limiting line. In all te five series of H - spectrum, te line of longest wavelengt is 1 st line of Pfund series (6 5) and te line of sortest wavelengt is limiting line of Lyman series( to 1) n(n + 1) = No.of possible spectral lines ; n = n n 1 As te value of 'n' increases i) te total energy of electron increases ii) te energy difference between te successive orbits decreases iii) P.E increases and K.E. decreases iv) radius of orbits increases v) velocity of electron decreases Merits of Bor's teory: He could explain te spectra of H - atom and oter single electron species like He +, Li + etc. He could determine frequency, wavelengt, wave number of lines in H - spectrum. He could calculate te value of Rydberg constant (R). He could determine energy and velocity of electron and radius of orbits. He could explain te stability of atoms tat is wy, electrons are not falling into te nucleus and atoms are not collapsed. Demerit's of Bor's teory: Bor failed to explain spectra of multi electron species. He failed to explain fine structure of te H-spectrum. He failed to consider te wave number of electron. Bor's teory contradicts Hisenberg's uncertainty principle. Quantum numbers: To fully explain te motion of electron and to locate it's correct address te following four quantum numbers are required. Principal quantum number (n) : It is proposed by Bor and denoted by 'n'. It represents te main energy level. It determines te size of te orbit and energy of te electron. It takes all positive and integral values from 1 to n. Te maximum number of electrons in a main energy level is n, and number of orbitals is n.

11 11 If n is te principal quantum number te energy of te electron in te principal quantum level is 4 π e m En = ; E n = n n ev/atom As te value of 'n' increases, te energy of electron increases. Te energy of electron in te ground state of ydrogen atom is 13.6 ev/atom(or).176 x10 11 erg per atom(or) joule per atom(or) 131 kj per mole (or) kcal per mole. Te energy of te electron in te second orbit of ydrogen atom is 13.6 = = 3.4 ev/atom Azimutal quantum number ( ): It is also known as angular momentum quantum number or orbital quantum number (or) subsidiary quantum number. To express te quantised values of te orbital angular momentum, azimutal quantum number was proposed. It is denoted by and takes values from 0 to n 1. Te number of values of is equal to te value of n. It explains fine structure in H-spectrum. It determines te sape of orbitals. More fine lines in eac main spectral line are seen. If n = 1, = 0 (s - sub-sell) If n =, = 0, 1 (s, p sub-sells) If n = 3, = 0, 1, (s, p, d sub-sells) If n = 4, = 0,1,, 3 (s, p, d, f - sub-sells) ( + 1) Te orbital angular momentum of electron = π Azimutal quantum number determines te sape of te orbital. Te number of orbitals in a sub sell is ( + 1). Te maximum number of electrons in a sub sell is ( + 1). Magnetic quantum number: To explain Zeeman and Stark effects Lande proposed magnetic quantum number. It is denoted by m. It represents te sub-sub energy level or atomic orbital. It determines te orientation of orbital in space. Wen te atom is placed in an external magnetic field, te orbit canges its orientation. Te number of orientations is given by te values of te magnetic quantum number m. m takes te values form to + troug 0. Total values of m for a given value of = ( + 1) values. A sub sell aving azimutal quantum number l, can ave ( + 1) space orientations. Te number of orbitals in a subseii = ( + 1). If te canges in te axis in one direction are indicated by + m values, te canges in te axis in te opposite direction are indicated by m. Spin quantum number (s):

12 1 In te fine spectrum of alkali metals pairs of widely separated lines are observed wic are different from duplet, triplet, and quadruplets observed in te ydrogen spectrum. To recognise and identify tese pairs of lines Goudsmit and Ulenbeck proposed tat an electron rotates or spins about its own axis. Tis results in te electron aving spin angular momentum, wic is also quantised. Te electron may spin clockwise or anti clockwise. Terefore, te spin quantum number takes two values +1/ and 1/. Clockwise spin or parallel spin is given +1/ or and anti clockwise or anti parallel spin is given by 1/ or. Wave nature of electron de-broglie teory: de-broglie proposed tat te dual nature is associated wit all te particles in motion and tey are called matter waves. Electrons, protons, atoms and molecules wic are treated as particles are associated wit wave nature. Correlating Planck's equation E = v and Einstein's equation E = mc, we can get wavelengt of matter waves. λ = mc = p = mv de-broglie applied tis condition for te material particles in motion. Te wavelengt of a particle in motion is inversely proportional to its momentum. Smaller particles wit very little mass ave significant wavelengt and bigger particles wit large mass ave negligible wavelengts. As electron as negligible mass, it as significant wavelengt. Te wave nature of electron was proved experimentally by Davisson and Germer in electron diffraction experiments. Hence electron exibits bot wave nature and particle nature. Bor's teory and de Broglie's concept: According to Bor, electronic motion is permitted wen te angular momentum is an integral multiple of /π. n mvr = π According to de Broglie, an electron beaves as a standing or stationary wave, wic extends round te nucleus in a circular orbit. If te two ends of te electron wave meet, te electron wave is said to be in pase. In oter words tere is constructive interference of electron waves and te electron motion as a caracter of standing wave or non-energy radiating motion. For te electron wave in pase, te circumference of te Bor's orbit sould be an integral multiple of te wavelengt of te electron wave. n n mvr = πr = ; πr = nλ λ = According to Bor's quantum condition, π ; mv ( mv ) Tus, de-broglie's teory and Bor's teory are in agreement wit eac oter. In case te circumference of te Bor's orbit (πr) is bigger or smaller tan nλ, te electron wave is said to be out of pase. Ten destructive interference of waves occurs causing radiation of energy.

13 13 Suc an orbit cannot exist. Heisenberg's uncertainity principle: It is impossible to determine te exact position and velocity of te electron accurately and simultaneously. If te position is certain ten te accurate determination of velocity is uncertain and vice-versa wic is called Heisenberg's uncertainity principle. Δx. Δp or Δx.m ΔV or Δx. ΔV 4π 4π 4πm If Δx = 0, Δv = infinity If Δv = 0, Δx = infinity Were Δx is uncertainity in position and Δp is te uncertainity in momentum. Te radius of an atom is of te order of m. Hence te uncertainity in te position of electron cannot be more tan m. Wen Δx = m. 6.6x = = 5.8x10 ms 4πmΔx Te uncertainity in velocity Δv = 4x3.14x9.1x10 x10 Tus te minimum uncertainity in it's velocity can not be less tan m\sec Te uncertainity is not of tecnical in nature but it lies in te nature of particle itself. Scrodinger's wave equation: Scrodinger's wave teory is te basis for te modern quantum mecanical model of te atom. Wen te exact position of te electron cannot be determined we can predict te probability of finding te electron around te nucleus. Tis teory takes two facts into account. 1) Wave nature of te electron ) Te knowledge about te position of an electron is based on its probability. It describes electron as a tree dimensional wave in te electric filed of positively carged nucleus. Scrodinger's wave equation describes te wave motion of electron along X, Y and Z axes. ψ ψ ψ 8π m (E U) ψ = 0 x y z In te above equation 'm' is te mass of electron, E is its energy, U is its potential energy, ψ is called wave function or amplitude of te electronic wave. Te above equation indicates te variation of te value of ψ along x, y and z axes. Since, te probability of finding electron can not be negative, ψ is replaced by ψ. ψ is te probability function of te electron and it denotes te electron cloud density around te nucleus. Te region or space around te nucleus were te probability of finding te electron is maximum (About 95%) is called an atomic orbital. Te probability of finding te electron in te nucleus is zero. Te probability of finding te electron in te radial space around te nucleus is called radial probability. Te probability function of electron is called D function. Tus radial probability or electron probability function, D = 4πr dr.ψ In ydrogen atom te probability of finding te electron is maximum at a distance 0.53 Å from te nucleus. Te probability of electron at a distance of 1.3 Å is zero in H-atom. 34

14 14 Te plane in wic te probability of finding te electron is zero is called node or nodal plane or nodal surface. Sapes of orbitals: Te sape of s-orbital is sperical and sperically symmetrical. It as no nodal planes. Te number of radial nodes for s-orbital = (n 1) p-orbital as dumb-bell sape. It as one nodal plane. Te tree p-orbitals are mutually perpendicular to one anoter. Eac p-orbital as one nodal plane. Te lobes are oriented along te respective axes. p x orbital is along te x-axis and its nodal plane is along yz plane. p y orbital is along te y-axis and its nodal plane is along xz plane. p z orbital is along te z-axis and its nodal plane is along xy plane. For p-orbital l = 1 m = 1, 0, +1 For p x orbital; m = +1 For p y orbital; m = 1, For p z orbital; m = 0; d orbital as 4 lobes and double dumb-bell sape. Eac d-orbital as nodal planes. d xy orbital is in te xy plane between x and y axes. d yz orbital is in te yz plane between y and z axes. d xz orbital is in te xz plane between x and z axes. d x y orbital is also in te xy plane but te lobes are oriented along x and y axes. d z orbital is along te z-axis. In d xy, d yz, d zx orbitals, te lobes are in between te respective axes. d x In y, dz orbitals, te lobes are along te axes. d z contains a ring called torus or collar or tyre of negative carge surrounding te nucleus in te xy plane. It as only big lobes oriented along z-axis. For d-orbital, I =, m =, 1, 0, +1, + d For z orbital, m = 0, for dxz orbital, m = +1 For d xy orbital, m = for d yz orbital, m = 1 d x For y orbital, m = + Te energy of electron in ydrogen atom is determined only by te principal quantum number n. In multi electron atoms, te energy of electron depends on bot principal quantum number and azimutal quantum number. Te magnetic quantum number m indicates te number of degenerate levels or orbitals of equal energy. An orbital aving a certain value for m cannot accommodate more tan electrons. Te maximum number of electrons in s, p, d and f sub energy levels is, 6, 10 and 14 respectively. Te maximum number of electrons in a given principal quantum level 'n' is n. Te maximum number of sub orbitals in a main orbit = n.

15 15 Te maximum number of orbitals in a main orbit = n. Te maximum number of orbitals in a sub orbit = (l +1). Te maximum number of e s in a sub orbit = 4l + Pauli's exclusion principle: No two electrons in te same atom can ave te same set of values for all te four quantum numbers. Two electrons in a given orbital ave te same values of n, I and m but differ in spin quantum numbers. Aufbau principle: Te orbitals are successively filled in te order of teir increasing energy. Among te available orbitals, te orbitals of lowest energy are filled first. Te relative energy of orbital can be known by (n+l) formula. If two orbitals ave te same value of (n + l), te orbital aving lower n value is first filled. As atomic number increases, (n + l) formula is not useful to predict te relative energies of orbitals a) for example, up to z = 0, 3d > 4s Beyond z = 0, energy difference narrows up. Beyond z = 57, 3d < 4s. b) upto to z = 57,4f > 5p beyond z = 57, 4f > 5p ; At z = 90, 4f < 5s. Te order of filling of orbitals can be known from Moellar's diagram. Hund's rule of maximum multiplicity: Orbitals aving te same values for n and are called degenerate orbitals. Pairing of orbitals will begin after te available degenerate orbitals are alf filled. Orbitals wit igest resultant spin value are more stable. Te degenerate orbtials are filled to ave like spins as far as possible. As per Hund's rule, te number of unpaired electrons in te ground state of C, N, O are, 3, respectively. In te absence of Hund's rule, te number of unpaired electrons in C, N, O are 0, 1, 0 respectively. Te filling of orbital is governed by Pauli's principle. Te filling of sub-orbit is governed by Hund's rule. Te filling of orbitals of various suborbits is governed by Aufbau principle. Te maximum number of electrons tat are present in te outer most sell of any atom = 8 Te maximum number of electrons tat are present in te (n 1) most sell of any atom = 18 Te maximum number of electrons tat are present in te (n ) most sell of any atom = 3 Anomolous electronic configurations: 1. Half filled and completely filled degenerate orbitals give greater stability to atoms.. Cromium (Z = 4) and copper (Z = 9) ave anamalous electronic configuration due to tis reason. 3. Electronic configuration of cromium atom is 1s s p 6 3s 3p 6 3d 5 4s 1 or [Ar] 3d 5 4s 1 but not 1s s p 6 3s 3p 6 3d 4 4s. 4. Electronic configuration of copper atom is 1s s p 6 3s 3p 6 3d 10 4s 1 or [Ar] 4s 1 3d 10 but not 1s s p 6 3s 3p 6 3d 9 4s. Magnetic properties:

16 Atoms molecules, ions or any species aving unpaired electrons exibit para-magnetism. Tese are attracted into te magnetic field wen tey are placed in an external magnetic field. Atoms aving te completely paired electrons are repelled by te external magnetic field and are called diamagnetic. Te unpaired electrons produce magnetic field in atoms due to teir resultant spin. Te magnetic moment of atoms containing unpaired electrons is given by te formula μ = n (n + ) B.M> Were 'n' is te number of unpaired electrons. Unit of magnetic moment is Bor magneton (B.M.) If n = 1, μ = 1 B.M, If n =, μ = B.M, If n = 3, μ = 3 B.M and so on. Stability of atoms: Teory of excange forces will explain wy Cr as (Ar) 3d 5 4s 1 but not (Ar) 3d 4 4s. According to tis teory, greater te number of unpaired electrons, greater is te number of possible excange pairs of electrons and more is te excange energy released and te atom is more stable. For C r (Ar) 3d 5 4s 1, te possible number of excange pairs = 15. If energy released for eac excange pair is k, te total excange energy is 15 k. For Cr (Ar) 3d 4 4s, te possible number of excange pairs = 10 and total excange energy is only 10k. Terefore Cr (Ar) 3d 5 4s 1 is more stable tan Cr(Ar) 3d 4 4s 16