tutorial on structure of atom class 11

STRUCTURE OF ATOM INTRODUCTION:- * The Name “Atom” was given by British Scientist – “John Dalton” (1808). He gave “The Atomic Theory”. According to him Atom was Indivisible. * By the help of various discoveries by many other scientists. Dalton’s concept that Atom is indivisible was proved wrong. * At present we know around 35 such particles which might be a component of as Atom. These 35 particles collectively are called “SUB-ATOMIC PARTICLES. Amongst them three are called the “FUNDAMENTAL PARTICLES”. The name of these 3 particles are:-(1) Electron(2) Proton(3) Neutron The description regarding the discovery and important characteristics of these 3 fundamental particles is:- 1. The Electron:- (a) The electron was discovered in “CATHODE RAYS EXPERIMENT” by J.J.Thomson.(b) The name “electron” was coined by G.J.STONEY,(c) The Charge on electron was determined by “R.A.MILLIKEN” by his experiment called “THE OIL DROP EXPERIMENT”.(d) The credit for the determination of “Actual Mass” of electron and various characteristics of cathode rays and discovery of electron goes to “J.J. Thomson”. * J.J. Thomson placed different gases in the cathode ray tube and calculated the charge to mass Ratio (e/m) of electron. The value was always found to be the same i,e. * Further Mulliken calculated the charge on electron to be( negative sign, denotes negative charge, although in calculations only magnitude is used So the mass of ē can be calculated as ∵ ē/m=1.76 X 108 C/g Or 1.6 X 10-19 C == 1.76 X 108 C/g m ∴ m = 1.6 X 10-19 C 1.76 X 108 c/g Or ∵ 1 g = 10-3 kg This is called Rest Mass of ē.(i.e , assuming it to be at rest). When it is moving with a velocity ‘V’ its mass m is given by m = m rest where c=velocity of light √1-v2/c2 (e) Radius of the ē is found to be of the order of 10-15 cm.(f) Density of ē is found to be 2.17 X 1017 gm/cm3. (g)Mass of one mole of ē is nearly = 0.55 mg (h)Charge on 1 mole of ē is = 96500 Coulombs = 1 FARADAY. (i) DEFINITION :- An ē is that fundamental particle which carries one unit –ve charge and has a mass nearly equal to 1/1837th of that of H- Atom. 2. The Proton:- (a) Discovered by the “ANODE RAYS EXPERIMANT “ by E. GOLDSTEIN”(1886). (b) Mass of a proton is found to be 1.672 X 10 -24 kg. (c) Charge on proton = +1.602 X 10-19 Columbs. = +4.8 X 10-10 e.s.u. (d)Specific charge of a Proton is:-p/m =9.58 X 10-14 C/g. However ,the specific charge is not constant for Anode Rays but changes with the gas in the tube. It is maximum when gas present in the discharge tube is “Hydrogen”. (e) 1 mole of Proton is nearly 1.007 g in mass. (f) Charge on 1 mole of Proton ≈ 96500C = 1F. (g) DEFINITION :- A Proton is that fundamental particle which carries unit positive charge and has a mass that is nearly equal to that of H- Atom. 3. The Neutron:- (a) The neutron was discovered by “JAMES CHADWICK” in 1932. (b) The reason for the late discovery of the Neutron was its Neutral Nature (c) Neutron is slightly heavier (0.18%) than Proton. Its mass is 1.675 X 10 -27 kg. or 1.675 X 10 -24 g. (d) Charge on Neutron is Zero. Hence, specific charge of a Neutron is also Zero. (e) Mass of 1 Mole of Neutron is nearly 1.008 g. (f) Density of a Neutron is nearly 1.5 X 10 -14 kg. (g) Of all the fundamental particles present in atom Neutron is the Heaviest & least stable particle. An isolated Neutron is unstable and disintegrates into electron , Proton and Neutron. TABLE :- Comparison of mass & Charge of the fundamental sub-atomic particle. NAME OF CONSTANT UNIT ELECTRON (e) PROTON (p) NEUTRON (n) MASS ⓜ u kg Relative 0.000549 9.11 X 10 -31 1/1837 1.00728 1.673 X 10 -27 1 1.00867 1.675 X 10 -27 1 CHARGE ⓔ Coulomb ⓒ e.s.u. Relative -1.602 X 10 -19 -4.8 X 10 -10 -1 +1.602 X 10 -19 +4.8 X 10 -10 +1 Zero Zero Zero 1 u = 1/12TH of the mass of a C-12-atom or 1 a.m.u. = 1 X 12g =1.6606 X 10-24g 12 6.022X1023 = 1.6606 X 10-27kg SOME UNCOMMON SUB-ATOMIC PARTICLES. 1. Positron:( Discovered by C.D. Anderson in 1932. ( very unstable ( Combines with ē to produce gamma(γ)-rays (energy radiation) ( has +ve charge ( mass equal to ē ( Represented as 1e0 or e+ 2.Mesons:( Discovered by YUKAWA in 1935. (These are of 2 types:- π- mesons or pions (b) μ-mesons or muons (These may be either +vely charged,-vely charged or neutral (Their mass is intermediate between that of an ē and Proton. They are roughly 200 times the mass of an ē. ( π- mesons are little heavier that μ-mesons. (To account for the binding forces between like particles such as Proton & Proton or Neutron and Neutron , KEMMER suggested the exhistance of a NEUTRAL MESON(π0) 3. Neutrino & Antineutrino:( These are particles of Zero charge. ( Their mass is not constant but is definitely less than that of an ē. ( Neutrino was discovered by PAULING in 1927. ( Antineutrino was discovered by FERMI in 1934. (Radius is also expressed in Fermi ( 1 Fermi = 10-15 m). Radius range = 1.5 Fermi to 6.5 Fermi ( Density of nucleus is of the order of 10-15 g/cm3 4. Antiproton:( Discovered by SEGRE in 1956 ( Posseses unit –ve charge. (Mass is equal to that of a Proton. MODELS OF ATOMS 1.Thomson Model Of Atom:-(1904) by J.J.Thomson. Its called RAISIN-PUDDING or WATERMELON MODEL .Where an atom is considered to be a +vely charged sphere with ē embedded in it here and there just like raisins in a pudding or seeds in a watermelon. “This model was later Rejected” 2. Rutherford’s Nuclear Model Of Atom –(The Discover Of Nucleus) Experimental Set-up:- A very thin foil(almost 100 nm thick) of heavy metals like Gold, Platinum Or Copper was bombarded with a beam of fast moving α -particles and their projection was studied on a circular Zinc Sulphide Screen. The point at which an α -particle Strikes this Screen, a flash of light is given out. Result:-( Most of the Atom is empty. (There is a small heavy +vely charged body present within the atom. This body was termed as the “NUCLEUS”. (The part of atom other than the Nucleus was termed as the “EXTRA-NUCLEAR PART”. This part has ē’s. (ē’s revolve around the nucleus just as planets around the sun and hence forth called PLANETARY ē’s. ( The radius of Nucleus is of the order of 10-15 m of atom 10-10 m. Atomic Number (Z) & Mass Number(A):- 1. ie, 2. ie, 3. ∵ p = Z ∵ A- Z = n ie, 4. General Symbolic representation for an element is:- ZEA or ZAE (E –Element) Some terms to remember a. Isotopes:- Such Atoms of the same element having same atomic Number but different mass Number are called Isotopes. 1.For Eg. Isotopes of Hydrogen: -Ⓗ 1H1 called “Protium” (p=1 , e=1, A=1, Z=1 n=0) Ⓓ 2H1 called “Deuterium” (p=1 , e=1, A=2, Z=1 n=1) Ⓣ 3H1 called “Tritium” (p=1 , e=1, A=3, Z=1 n=2) 2. Isotopes of chlorine :- 35Cl17 37Cl17 ( The term “Isotope” was coined by “SODDY” ( Isotope was first separated by “ASTON” using mass spectrometer (Ne20 , Ne22) ( Of all the elements, Tin (Sn) has the maximum Number of stable Isotopes(Ten). b. Isobars:-Such Atoms of different elements which have the same mass numbers and obviously different Atomic Number are called Isobars. For Ex. 40Ar18, 40K19, 40Ca20 c. Isotones:-Such Atoms of different element which Contain the same Number of neutrons are called Isotones. For Ex. 14C6, 15N7, 16O8 d. Isodiaphers :-Such Atoms having the same Isotopic Number( or Isotopic Excess) are called Isodiaphers. Mathematically, Isotopic Number= N-Z or A-2 Z Where N= No. of neutrons, A=Mass No., Z= Atomic No. For Ex. :- 235U92 and 231Th90 , 39K19 and 19F9 , 65Cu29 and 55Cr24 e. Isoelectronics or Isoelectronic Species:-Species(atoms, molecules or ion)having same Number of ē are called Isoelectronics. For Ex:- N3-, O2-, F-, Ne, Al3+, CH4 all have 10 ē. f. Isosters:-Molecules having same number of atoms and also same number of ē are called Isosters. For Ex:- N2 and CO, CO2 and N2O g. Nuclear Isomers:-Such atoms with the same atomic Number and same mass number but with different radioactive properties are called Nuclear Isomers. Nuclear Isomers were discovered by OTTO HAHN. For Ex:- URANIUM – M (half life – 1.4 minutes) , URANIUM – Z (half life – 6.7 hours) Drawbacks Of Rutherford’s Model:- According to clark Maxwell a charged particle moving under the influence of attractive force continuously looses energy in the form of electromagnetic Radiations. Thus, the ē(a charged body) moving around the nucleus must emit radiations and gradually lose energy. Due to its loss of energy, its motion would slowdown and therefore, it may not be able to withstand the attraction of the nucleus. Consequently the ē would fall into the nucleus. Working on this principle Bohr calculated that an atom would collapse in 10-8 seconds. But since atom is quite stable and such a collapse of the atom does not take place there must be some drawback in the Rutherford’s model of an atom. Further rutherford’s model could not explain the characteristic of emission Spectra by all the elements. --------------------------------------------------------------------------------------------------------------------------------------- ۞ The next revolutionary model of atom was given by BOHR was but before proceeding to his model it is important to study the “Dual nature of light” which was also an important subject of concern in his model since spectrum deals with light. So light is considered to have wave nature as well as particle nature. Two most accepted theories regarding dual nature of light are discussed below- --------------------------------------------------------------------------------------------------------------------------------------- ELECTROMAGNETIC WAVE THEORY:- *The Radiations consist of electric and magnetic fields oscillating perpendicular to each other and both perpendicular to the direction of propagation of radiations. * Electromagnetic Radiations do not require any medium for propagation. * These have wave characteristics. Every electromagnetic wave have 5 characteristics:- 1. Wavelength(λ):- Wavelength determines the color of a beam of visible light.[unit Ả, cm or m] 2. Frequency(υ):- [unit hz or cycles per sec] 3. Velocity(c) :- All electromagnetic radiations/waves travel with the same velocity; the velocity of light i.e 3x108 m/s or 186000 miles/s 4. Wave number(ΰ) :- ΰ=1/ λ 5. Amplitude:- According to electromagnetic wave theory the energy of an electromagnetic wave is directly proportional to the brightness or intensity of light which in turn is directly proportional to the square of the amplitude, i.e Energy α Intensity α (amplitude)2 * ELECTROMAGNETIC SPECTRUM:- The arrangement of the various types of electromagnetic Radiations in order of their increasing ( or Decreasing) wavelengths (or Frequencies) is known as “Electromagnetic Spectrum”. Electromagnetic Radiation Wavelength(A) Frequency(Hz of Sec-1) RADIOWAVES 3x1014 to 3x107 1x105 to 1x109 MICROWAVES 3x107 to 3x106 1x109 to 5x1011 INFRARED[IR] 6x106 to 7600 5x1011 to 3.95x1014 VISIBLE 7600 to 3800 3.95x1014 to 7.9x1014 ULTRAVIOLET[UV] 3800 to 150 7.9x1014 to 2x1016 X-RAYS 150 to 0.1 2x1016 to 3x1019 GAMMA RAYS 0.1 to 0.01 3x1019 to 3x1020 COSMIC RAYS 0.01 to Zero 3x1020 to Infinity *Energy Of Radiation E α I α a2 Electromagnetic Wave Theory:- ( This theory was put forward by James Clark Maxwell ( According to this theory the energy is emitted from any source(like the bulb or heater, arc etc.) ( Continuously in the form of radiations (or waves) and is called the “RADIANT ENERGY”. These are electromagnetic radiations. Limitations Of Electromagnetic Wave Theory:- This theory was successfully able to explain the wave nature properties of light such as INTERFERENCE, DIFFRACTION etc. but could not explain the following:-(1)The Phenomenon of “Black Body Radiation”:- If any substance with high melting point (e.g. an iron bar) is heated it first becomes red, then yellow and finally beings to glow with white and then blue light. This shows that wavelength of frequency changes with Energy. Whereas according to the electromagnetic wave theory the energy of radiation E α I(Intensity) α a2 (amplitude)2. i.e., E is independent of λ or υ hence color of flame must remain the same. Hence this theory could not explain this phenomenon. Definition:- If the substance being heated is a “Black Body”(which is a perfect absorber and perfect Radiator of energy ie, which can emit and absorb all frequencies) the Radiations emitted is called “Black Body Radiation”. (2) The Photoelectric Effect:- When a beam of Radiations of sufficiently high frequency is allowed to strike a metal surface in vacuum, electrons are ejected from the metal surface. This phenomenon is called “Photoelectric Effect” and the ejected electrons as “Photoelectrons”. Here again it has been observed that the change in the intensity of incident radiation does not alter the Energy of electrons, whereas a change in frequency (or wavelength) does. So again, Electromagnetic wave theory is unable to explain this phenomenon. (3) The variation of heat capacity of solids as function of temperature. (4) The line spectra of atom with special reference to hydrogen. (5) The Compton Effect:- When X-Rays are allowed to fall on lighter elements like Carbon, wavelengths of scattered X-Rays are found to be larger than that of incident X-Rays. i.e, This phenomenon is called the COMPION EFFECT. This also could not be explained by wave theory. All these mentioned phenomenon could only be explained if Electromagnetic waves are supposed to have “PARTICLE NATURE” Particle Nature Of Electromagnetic Radiation:-> Planck’s Quantum Theory. To explain or rather overcome the above mentioned limitation of the wave Nature of Electromagnetic Radiations, MAX PLANCK in 1990, put formed this theory called “The Quantum Theory”. This theory was further extended by Einstein in 1905. According to this Theory:- (1) The Radiant energy is emitted or absorbed not continuously but discontinuously in the form of small discrete packets of energy. Each such packet of energy is called a “Quantum”. In case of light the Quantum of energy is called a “PHOTON”. (2) The Energy of each Quantum is proportional to the frequency of the radiation. E α υ or h= Planck’s Constant = 6.626 X 10-27 ergs sec = 6.626 x 10-34 joule sec [1erg = 10-7 Joule] (3) The total amount of energy emitted or absorbed by a body will be some whole number Quanta where n is an integer ie., 1,2,3,………………….. planck’s Quantum theory could successfully explain Black Body Radiations, the photoelectric effect., Compton effect etc. Hence it can be concluded that some phenomenon of “LIGHT” (or in general any electromagnetic radiations) could be explained by its “Wave Nature” while other by its “Particle Nature”. So we can say that light has “Dual Nature”. This idea was put forward by EINSTEIN in 1905 Explanation for Black Body Radiation. As the solid substance is heated its atoms start oscillating and as more and more energy is imparted then frequency and henceforth energy increases. Since red color has minimum frequency and blue the maximum. It explains the color changes of flame from Red to Blue. Explanation For Photo electric effect:-(1) The electron from metal is detached only if the energy ie., the frequency of Photon is large enough to overcome the force of attraction between the electron and nucleus of the metal. This is the explanation for threshold frequency. (2) If incident frequency (υ) is greater than threshold frequency(υ0). Then incident energy is imported as Kinetic energy to the electrons. ie. ½ mv2 = h υ – h υo ½ mv2 = h υ – Wo h υ = ½ mv2 + Wo ie. greater is the frequency greater is the KE imparted. Here W0 is called work function or Threshold energy which is specific for every metal. Bohr’s Model Of Atom:- Neils bohr, in 1913, proposed a theory of “hydrogen atom” which overcame the drawbacks of Rutherford’s model. It could explain the origin of Hydrogen spectrum. This theory was based upon some postulations from “classical Mechanics” and some from “Planck’s Quantum Theory” Postulates Of Bohr’s Model:- (i)An atom consists of a small , heavy , positively charged nucleus in the centre and the electrons revolve around it in circular orbits. (ii) The electrons revolve in orbits called the “Stationary Orbits”. In these orbits the electron revolves but neither loses nor gain energy. These orbits are numbered 1,2,3,4…………….etc. or K,L,M,N……..etc. (iii) Bohr’s formula for Energy, Radii of Orbit & velocity of electron are explained in next segment. (iv) Energy of electron is Quantized (v) The angular momentum of the electron is an integral multiple of h/2π.ie. angular momentum (L)=Momentum Of Inertia(I) x Angular Velocity(w) L is also Quantized (vi) The lowest energy state is called “NORMAL” or “GROUND STATE” (vii) All other higher energy states are of higher energy & are called “EXCITED STATES”. These are unstable. (viii) Energy is released when electron drops from excited state to ground state in the form of light. (ix) Energy is absorbed vice versa. (x) Change in energy ∆E=E2-E1. The Emission Spectrum Of Hydrogen:- The emission spectrum of hydrogen is found to consist of a large number of lines which are grouped into different series, named after the discoverers. These series are:- LYMAN SERIES- UV Region BALMER SERIES- Visible Region PASCHENSERIES- Infrared Region BRACKETTSERIES-Infrared Region PFUNDSERIES- Infrared Region HUMPHRYSERIES- Far Infrared Region These pattern of lines in atomic spectrum are characteristic for Hydrogen atom(i.e., every sample of hydrogen gives the same spectrum) & is different from that of any other element. Thus, in general, atomic spectra are referred to as the finger prints of the atoms. Advantages of Bohr’s Theory:- Bohr’s theory satisfactorily explains the spectra of species having one ē like Hydrogen atom, He+, Li+2 ,etc. further it also can be used for calculating :- (1) Radius of various orbits of Hydrogen like species. (2) The velocity of ē with which it revolves in various orbits of hydrogen like species. (3) The energy of ēs moving in different orbits around nucleus in hydrogen like species. Applications Of Bohr’s Model:-(1)Calculation Of Radius Of The Bohr’s orbit:- Consider an ē of mass “m” & charge “e” revolving around the Nucleus of charge Ze(Z being the atomic number & e being the charge on a proton) with a tangential velocity “v”. Further suppose “r” is the Radius of the orbit in which ē is revolving. Then by coulomb’s law, the electrostatic force of attraction (Fe) between the moving ē & Nucleus is:- Where k is a constant & is value is given by k=1/4πεo where εo is the permittivity in free space :- Now, since the electrostatic force balances the centrifugal force, for the stable ē orbit According to Bohr;s postulates angular momentum of ē is expressed as :- Here h=6.626 x 1034 Js m=9.1 x 10-31 Kg π= 3.14 k= 9 x 109 NM2/C2 e= 1.6 x 10 -19 C i.e., r α n2 putting all these values in equation (8) we get (2) Calculation Of Vilocity Of ē In Bohr’s Model:- i.e., v α 1/n (3)Calculation Of Energy Of an ē In Bohr’s Model:- The total energy of an ē revolving in a particular orbit is calculated by adding its potential & kinetic energy. So, The Kinetic energy of ē = ½ mv2 The Potential energy of ē = -KZe2/ r since 1ev = 1.6x10-19 J, or 1J = 6.25 x 1018 ev Explation For Line Emission Spectrum Of Hydrogen On The Basis Of Bohr’s Model Of Atom:- (1) Calculation Of Frequency Of Emitted Radiation:- Maximum number of lines produced when the ē jumps from nth level to ground level is n(n-1) 2 Consider the ē drops from a higher energy level n2 to a lower energy level n1 , then Hυ = En2 – En1 --------(1) When En2 & En1 are the energies of n2 & n2 energy levels respectively here, Limitations Of Bohr’s Model Of Atom:- (1) It only explain the spectrum of species having are ē. (2) It cannot explain the fine structure of H-spectrum. (3) No justification is give for the principle of Quantization of angular momentum. (4) It does not explains the splitting of spectral lines under the influence of electric field(STARK EFFECT) & magnetic field(ZEEMAN EFFECT). (5) This model is unable to explain the Heisenbergs uncertainity principle & do Broglies concept of dual Nature of matter. Dual Nature Of Matter:- The De Broglie Concept:- According to the Planck’s Quantum theory, for a Photon having wave character energy:- E = h υ------(1), if photon is supposed to have particle character, its energy is particle by Eiusteins equation, which is:- E = m c2------(2) Comparing equation (1) & equation (2) we get h υ = m c2 but υ = c λ ( h c = mc2 or λ = h .----------(3) λ mc de Broglie pointed out that the above equation is applicable to any material particle. ( This is called de-Broglie equation. A λ is de-Brogle wavelength. Waves associated with matter are called Matter Waves. Calculation Of De-Broglie Wavelength Of The ē From The Potantial Applied To Accelerate It:- Derivation Of Bohr’s Postulate Of Quantization Of Angular Momentum From de-Broglie Equation:- According to de-Broglie ē not only possesses particle character but also wave character. So while revolving in circular orbit, the wave related to ē must be completely in phase with the circumference of the orbit i.e., 2 π r = n λ ------(1) i.e., wavelength must be an integral multiple of circumference . according to de-Broglie equation:- Equation (3) is Bohr’s postulate of angulat momentum. HEISENBREG’s UNCERTAINTY PRINCIPLE:- According to this principle, it is impossible to specify at any given moment both the position & momentum (velocity) of an ē. (x. (p >= h/4π or This ----(1) or (x.m (v = h/4π or ---(2) This principle also holds significance only for microscopic objects. In view of Hiesenberg’s principle, Bohr’s model in which ēs are considered as particles revolving in definite orbitals i.e., in well defined paths cannot hold good. Therefore, an ē is associated with a definite energy, i.e., it belongs to a definite ENERGY LEVEL & not that it belongs to a particular orbit. Wave Machanical Model Of Atom:- When, the position & momentum or an ē at a particular time cannot be known accuately, it is meaningless to think of sharply defined path i.e., orbit in Bohr’s model of moving ēs. Instead, it is possible only to predict or state the PROBABILITY of locating an ē of a particular energy in a given region of space at a given time. Quantum Mechanics was developed by ERWIN Schrodinger for the wave motion of ē I the three Nucleus, he put forward the following equation, known as Schrodinger Wave Equation. The solution of schrodinger wave equation gives the values of Quantized energy of ē & ψ the values of corresponding wave function. Here the values of E & ψ are called eigen values & eigen unctions. Ψ be considered as amptitude of wave of ē, Probability α Ψ2 or electron density The region around the nucleus which represents the ē density at different points is called an orbital. That is why the wave function associated with an orbital is called an “Orbital wave function” or simply an “Atomic Orbital”. Probability provides the best possible description of a situation which cannot be described with certainty. The region of space around the Nucleus which describes the probability energy, in terms of dots is called an “ē cloud”. An atomic orbital is that three dimensional space around the nucleus without which the probability of finding an ē of a given energy is maximum (upto 90%) comparison of orbit & orbital. Orbit:- (1)It is a well defined circular path around the nucleus in which the ēs revolve.(2) it represented the planer motion of an ē around the nucleus. (3) The concept of an orbit is not in accordance with the wave Nature of ē & Heisenbergs uncertainty principle.(4) all orbits are circular & disk like.(5) Orbits do not have any directional characteristics. (6) The maximum no. of ē in an orbit is given by 2n2+ where “r” is the no. of the orbit. Orbital:-(1) It is the three dimensional space around the nucleus within which the probability of finding an ē is maximum (upto 90%).(2) It represented the three dimensional motion of an ē around the nucleus.(3) The concept orbitals have different shapes.(5) All orbitals except s-orbital have directional characteristic. (6) The maximum no. of ēs presented in any orbital is Quantum Numbers:- Quantum Numbers are set of four numbers with the help of which we can get complete information about all the ēa in an atom. i.i., location energy, the type of orbital occupied shape & orientation of that orbital etc. Quantum Numbers Are Four Types:- (1) Principla Quantum Number:- (1) It was proposed by Bohr. (2) Represented by ‘n’. (3) It gives the information of the approximate difference of the ē from the nucleus i.e., Size of the ē cloud.(4) Since the ē clouds are three dimensional, the word “SHELL” is preferred over orbit or level. The energy of the ē present in any shell. En = -1312 Z2/n2 KJ/Mole. (5) Maximum number of ēs in a given shell in 2n2 where n= 1,2,3,4……(6) It helps to explain the main lines of H- spectrum.(7) Although theoretically its value may be from 1 to (, only values from 1 to 7 have so far been established for atoms of the main ** elements. (2) Azimuthal/ Subsidiary/ Angular Mumentum Quantum Number:- (1) It was proposed by sommerfield.(2) Represented by ‘l’. (A part of the energy of the ē which is circulated by ‘n’ is due to the angular momentum of the ē. Since different ēs have different “angular momenta”, the ēs within the same shell occupy different energy levels called‘Sub–Level’ or ‘Sub-Shells’). So ‘l’ gives the following information.(i) The number of the subshells present within any main shell.(ii) Contribution of the energy due to Angular momentum towards the total energy of the ē.(iii) Relative energies of the subshells belonging to the same shell.(iv) Shapes of the subshells.(v) Orbital angular momentum which is equal to=h(l( l+1) 2π (vi) It helps to explain the fine lines of the spectrum because due to the presence of a large number of subshells the number of probable transitions(jumps) of ē becomes very large.(vii) For a given value of “n”,”l” can have values Ranging from 0 to n-1 ex:- for n = 1 ; l = 0 i.e., only 1 value. for n = 2 ; l = 0,1 i.e., only 2 value. for n = 3 ; l = 0 ,1,2 i.e., only 3 value. for n = 4 ; l = 0,1,2,3 i.e., only 4 value. So we can conclude that nth shell has n number of subshells. Also For l= 0 ,subshell is called ‘s’,for sharplining spectrum For l= 1 ,subshell is called ‘p’,for principle spectrum For l= 2 ,subshell is called ‘d’,for diffused spectrum For l= 3,subshell is called ‘f’,for fundamental spectrum Their representater is nl hence we can conclude Shell (n) Subshells Present 1(K) 1s 2(L) 2s 2p 3(M) 3s 3p 3d 4(N) 4s 4p 4d 4f (viii)The energies of these subshells are of the order as follows:- s < p < d < f (ix) The maximum numbers of ēs that can be held by these subshells is given as -2(2l + 1) ( l = 0 i.e., s ( 2 l = 1 i.e., p(6 l = 2 i.e., d ( 10 l = 3 i.e., f(14 & so on. (3) Magnetic Quantum Number:- (i) it was proposed by lande.(ii) Represented by ‘m’.[one of the major drawback of the Bohr’s model was that it was unable to describe the “Zeeman Effect” according to which the spectrum lines].(iii) In general for each value of l there can be 2l+1 values of m. pz ,py ,px ,dxy ,dyz ,dz2 ,dzx ,dx2-y2 m=0 ,-1 ,+1 ,-2 ,-1 ,0 ,+1 ,+2 Shapes Of Orbitals:- SACHIN GOYAL M.Sc. M.Phil (chem..)9414327939 Class-XI STRUCTURE OF ATOM 11 Charge = e =1.76x 108 C/g mass m Charge = e =-1.6x 10-19 C = -4.8 x 10-10e.s.u m = 9.11 X 10 -28 g 9.11 X 10 -31 kg p = e = Z No. Of Protons =No. Of Electrons = Atomic Number A = n + p Mass No. =No. Of Neutrons + No. Of Protons Mass No. – Atomic No. = No. Of Neutrons RADIUM BLOCK OF LEAD SLIT CIRCULAR ZnS SCREEN α- RAYS THIN FOIL OF GOLD MOST OF THE α-PARTICLES STRIKE HERE λscattered > λincident E scattered < Eincident υ scattered < υ incident E=h υ E= nh υ λ = h . = h . i.e., λ α 1 m υ P P λ = 1.2256X 10 -9 m ( V (x. (p ≈ h/4π-- (x. (v = h/4πm