Chapter 2 Structure of Atom PDF

60 36 Structure of atom E3 Chapter 2 Structure of atom (ii) Cathode rays produce mechanical effect, as they can rotate the wheel placed in their path. (iii) Cathode rays consist of negatively charged particles known as electron. (iv) Cathode rays travel with high speed approaching that of light (ran...

60 36 Structure of atom E3 Chapter 2 Structure of atom (ii) Cathode rays produce mechanical effect, as they can rotate the wheel placed in their path. (iii) Cathode rays consist of negatively charged particles known as electron. (iv) Cathode rays travel with high speed approaching that of light (ranging between D YG Composition of atom U ID John Dalton 1808, believed that matter is made up of extremely minute indivisible particles, called atom which can takes part in chemical reactions. These can neither be created nor be destroyed. However, modern researches have conclusively proved that atom is no longer an indivisible particle. Modern structure of atom is based on Rutherford’s scattering experiment on atoms and on the concepts of quantization of energy. The works of J.J. Thomson and Ernst Rutherford actually laid the foundation of the modern picture of the atom. It is now believed that the atom consists of several sub-atomic particles like electron, proton, neutron, positron, neutrino, meson etc. Out of these particles, the electron, proton and the neutron are called fundamental subatomic particles and others are non-fundamental particles. U Electron (–1eo) ST (1) It was discovered by J.J. Thomson (1897) and is negatively charged particle. Electron is a component particle of cathode rays. (2) Cathode rays were discovered by William Crooke's & J.J. Thomson (1880) using a cylindrical hard glass tube fitted with two metallic electrodes. The tube has a side tube with a stop cock. This tube was known as discharge tube. They passed electricity (10,000V) through a discharge tube at very low pressure ( 10 2 to 10 3 mm Hg). Blue rays were emerged from the cathode. These rays were termed as Cathode rays. (3) Properties of Cathode rays (i) Cathode rays travel in straight line. 10 9 to 10 11 cm/sec) (v) Cathode rays can cause fluorescence. (vi) Cathode rays heat the object on which they fall due to transfer of kinetic energy to the object. (vii) When cathode rays fall on solids such as Cu, X  rays are produced. (viii) Cathode rays possess ionizing power i.e., they ionize the gas through which they pass. (ix) The cathode rays produce scintillation on the photographic plates. (x) They can penetrate through thin metallic sheets. (xi) The nature of these rays does not depend upon the nature of gas or the cathode material used in discharge tube. (xii) The e/m (charge to mass ratio) for cathode rays was found to be the same as that for an e  (1.76  10 8 coloumb per gm). Thus, the cathode rays are a stream of electrons. (xiii) According to Einstein’s theory of relativity, mass of electron in motion is, m  Rest mass of electron(m )  [1  (u / c) 2 ] Structure of atom Where u = velocity of electron, c= velocity of and observed the formation of anode rays. These rays also termed as positive or canal rays. light. When 37 u=c than mass of moving electron =. (3) Properties of anode rays (i) Anode rays travel in straight line. Proton (1H1, H+, P) (ii) Anode rays are material particles. (1) Proton was discovered by Goldstein and is positively charged particle. It is a component particle of anode rays. (iii) Anode rays are positively charged. (2) Goldstein (1886) used perforated cathode in the discharge tube and repeated Thomson's experiment Proton(p+) Neutron(n) Amu 0.000546 1.00728 1.00899 –31 Kg Charge(e) Density –27 9.109 × 10 1/1837 1 Coulomb (C) – 1.602 × 10–19 Relative –1 C/g 1.76 × 108 Gram / cc 1 +1.602 × 10–19 –10 – 4.8 × 10 1.675 × 10–27 1.673 × 10 Relative Esu Specific charge (e/m)  Electron(e–) E3 Mass (m) Unit Zero –10 +4.8 × 10 2.17  10 17 The atomic mass unit (amu) is 1/12 of the mass of an individual atom of 6C Zero +1 Zero 9.58 × 104 Zero 1.114  10 14 1.5  10 14 ID Name of constant 60 Table : 2.1 Comparison of mass, charge and specific charge of electron, proton and neutron 12 , i.e. 1.660  10 27 kg. Particle Symbol Nature U Table : 2.2 Other non fundamental particles Charge esu 10  e , 1e ,  0  + Mass Discovered by (amu) + 4.8029 0.0005486 Anderson (1932) Pauli (1933) and Fermi (1934) D YG Positron –10  0 0 < 0.00002 p – – 4.8029 1.00787 Positive mu meson  + + 4.8029 0.1152 Yukawa (1935) Negative mu meson  – – 4.8029 0.1152 Anderson (1937) Positive pi meson  + + 4.8029 0.1514 Negative pi meson  – – 4.8029 0.1514 Neutral pi meson 0 0 0 0.1454 Neutrino ST U Anti-proton (iv) Anode rays may get deflected by external magnetic field. (vii) Unlike cathode rays, their e/m value is dependent upon the nature of the gas taken in the tube. It is maximum when gas present in the tube is hydrogen. Powell (1947) (viii) These rays produce flashes of light on ZnS screen. Neutron (on1, N) (v) Anode rays also affect the photographic plate. (vi) The e/m ratio of these rays is smaller than that of electrons. Chamberlain Sugri (1956) and Weighland (1955) (1) Neutron was discovered by James Chadwick (1932) according to the following nuclear reaction, 4 Be 9  2 He 4 6 C 12  o n 1 or 5 B 11  2 He 4 7 N 14  o n 1 38 Structure of atom (2) Neutron is an unstable particle. It decays as follows,  1 H 1  Proton 0 1 e electon  0 0 antinutrin o (iv) Two different elements identical atomic number. Atomic number, Mass number and Atomic species (1) Atomic number or Nuclear charge (i) The number of protons present in the nucleus of the atom is called atomic number (Z). s 1 Z Where,   X  ray’s frequency Fig. 2.1 of the metal a&b Mass number (A) = Number of protons or Atomic number (Z) + Number of neutrons or Number of neutrons = A – Z. are (ii) The atom of an element X having mass number (A) and atomic number (Z) may be represented by a symbol, Z XA. Table: 2.3 Different types of atomic species Atomic species (Soddy) Similarities Differences (i) Atomic No. (Z) (i) Mass No. (A) (ii) No. of protons (ii) No. of neutrons (iii) No. of electrons (iii) Physical properties (iv) Electronic configuration Examples (i) 11 H , 12 H , 13 H 16 17 18 8 O, 8 O, 8 O (ii) 35 17 (iii) 37 Cl , 17 Cl U (v) Chemical properties ID Isotopes D YG (vi) Position in the periodic table Isobars (i) Mass No. (A) (i) Atomic No. (Z) (i) (ii) No. of nucleons (ii) No. of protons, electrons and neutrons (ii) 40 18 40 Ar , 19 K , 40 20 Ca 130 52 130 Te , 130 54 Xe , 56 Ba (iii)Electronic configuration (iv) Chemical properties (v) Position in the perodic table. ST U No. of neutrons Isotones Isodiaphers have (2) Mass number E3 Z= atomic number constant. never (i) Since mass of a proton or a neutron is not a whole number (on atomic weight scale), weight is not necessarily a whole number. (ii) It was determined by Moseley as,   a(Z  b) or aZ  ab can 60 1 0n neutron (iii) Atomic number = Number of positive charge on nucleus = Number of protons in nucleus = Number of electrons in nutral atom. (i) Atomic No. (i) (ii) Mass No., protons and electrons. (ii) (iii) Electronic configuration (iii) 3 1 (iv) Physical and chemical properties (iv) 13 14 6 C, 7 30 14 31 32 Si , 15 P, 16 S 39 19 K , 40 20 Ca H , 42 He N (v) Position in the periodic table. Isotopic No. (i) At No., mass No., (N – Z) or (A – 2Z) electrons, protons, neutrons. (ii) Physical and chemical properties. (i) 92 U 235 , 90 Th 231 (ii) (iii) 19 K 39 , 9 F 19 29 Cu 65 , 24 Cr 55 Structure of atom (i) No. of electrons 39 (i) N 2 O, CO 2 , CNO  (22 e  ) At. No., mass No. (ii) Electronic configuration (ii) CO , CN  , N 2 (14 e  ) Isoelectronic species (iii) H  , He , Li  , Be 2  (2e  ) (iv) P 3  , S 2  , Cl  , Ar , K  and Ca 2  (18 e  ) (i) N 2 and CO (ii) No. of electrons (ii) CO 2 and N 2 O 60 (i) No. of atoms (iii) Physical and chemical properties. Isosters (iii) HCl and F2 (iv) CaO and MgS E3 (v) C6 H 6 and B3 N 3 H 6 denoted by the symbol  (nu) and is expressed in terms of cycles (or waves) per second (cps) or hertz (Hz). Electromagnetic radiations   distance travelled in one second = velocity =c   c  ID (1) Light and other forms of radiant energy propagate without any medium in the space in the form of waves are known as electromagnetic radiations. These waves can be produced by a charged body moving in a magnetic field or a magnet in a electric field. e.g.   rays,   rays, cosmic rays, ordinary light rays etc. (iii) Velocity : It is defined as the distance covered in one second by the wave. It is denoted by the letter ‘c’. All electromagnetic waves travel with the U same velocity, i.e., 3  10 10 cm / sec. (2) Characteristics D YG (i) All electromagnetic radiations travel with the velocity of light. (ii) These consist of electric and magnetic fields components that oscillate in directions perpendicular to each other and perpendicular to the direction in which the wave is travelling. (3) A wave is always characterized by the following five characteristics, U (i) Wavelength : The distance between two nearest crests or nearest troughs is called the wavelength. It is denoted by  (lambda) and is measured is terms of centimeter(cm), angstrom(Å), Crest micron(  ) or nanometre (nm). Wavelengt h ST Vibrating source Trough 1nm  10 cm  10 9 (iv) Wave number : This is the reciprocal of wavelength, i.e., the number of wavelengths per centimetre. It is denoted by the symbol  (nu bar). It is expressed in cm 1 or m 1.   1  (v) Amplitude : It is defined as the height of the crest or depth of the trough of a wave. It is denoted by the letter ‘A’. It determines the intensity of the radiation. The arrangement of various types of electromagnetic radiations in the order of their increasing or decreasing wavelengths or frequencies is known as electromagnetic spectrum. Table: 2.4 Energy Fig. 2.2 m ; 1cm  10 Å  10   10 nm 8 4 Name Radio wave Wavelength (Å) Frequency (Hz) 3  10 14  3  10 7 1  10 5  1  10 9 Microwave 3  10 7  6  10 6 1  10 9  5  10 11 Infrared (IR) 6  10 6  7600 7600  3800 5  10 11  3.95  10 16 3.95  10 16  7.9  10 14 Ultraviolet (UV) X-Rays 3800  150 7.9  10 14  2  10 16 150  0.1 2  10 16  3  10 19   Rays 0.1  0.01 3  10 19  3  10 20 Cosmic Rays 0.01- zero 3  10 20  infinity Visible 1 Å  10 8 cm  10 10 m ; 1  10 4 cm  10 6 m ; 7 c    3  10 10 cm / sec 7 (ii) Frequency : It is defined as the number of waves which pass through a point in one second. It is 40 Structure of atom Atomic spectrum - Hydrogen spectrum Atomic spectrum Spectrum is the impression produced on a photographic film when the radiation (s) of particular wavelength (s) is (are) analysed through a prism or diffraction grating. Types of spectrum (2) This model failed to explain the line spectrum of an element and the scattering experiment of Rutherford. Rutherford's nuclear model gave the following experiment, (i) Most of the observations D YG Hydrogen spectrum (1) Hydrogen spectrum is an example of line emission spectrum or atomic emission spectrum. on this deflection. (ii) Some of them were deflected away from their path. (iii) Only a few (one in about 10,000) were returned back to their original direction of Deflecte propagation. d particles -rays U (2) Absorption spectrum : Spectrum produced by the absorbed radiations is called absorption spectrum. based   particles passed without any ID (ii) Line spectrum : If the radiation’s obtained by the excitation of a substance are analysed with help of a spectroscope a series of thin bright lines of specific colours are obtained. There is dark space in between two consecutive lines. This type of spectrum is called line spectrum or atomic spectrum.. 60 (i) Continuous spectrum : When sunlight is passed through a prism, it gets dispersed into continuous bands of different colours. If the light of an incandescent object resolved through prism or spectroscope, it also gives continuous spectrum of colours. (1) Rutherford carried out experiment on the bombardment of thin (10–4 mm) Au foil with high speed positively charged   particles emitted from Ra and E3 (1) Emission spectrum : Spectrum produced by the emitted radiation is known as emission spectrum. This spectrum corresponds to the radiation emitted (energy evolved) when an excited electron returns back to the ground state. +ve Nucleus Fig. 2.4 ZnS screen (2) When an electric discharge is passed through hydrogen gas at low pressure, a bluish light is emitted. (2) From the above observations he concluded that, an atom consists of (4) All these lines of H-spectrum have Lyman, Balmer, Paschen, Barckett, Pfund and Humphrey series. These spectral series were named by the name of scientist discovered them. (i) Nucleus which is small in size but carries the entire mass i.e. contains all the neutrons and protons. U (3) This light shows discontinuous line spectrum of several isolated sharp lines through prism. ST (5) To evaluate wavelength of various H-lines Ritz introduced the following expression,   1   1 1   R 2  2  c  n1 n 2   Where R is universal constant known as Rydberg’s constant its value is 109, 678 cm 1. (ii) Extra nuclear part which contains electrons. This model was similar to the solar system. (3) Properties of the nucleus (i) Nucleus is a small, heavy, positively charged portion of the atom and located at the centre of the atom. (ii) All the positive charge of atom (i.e. protons) are present in nucleus. Plum pudding model of Thomson (iii) Nucleus contains neutrons and protons, and hence these particles collectively are also referred to as nucleons. (1) He suggected that atom is a positively charged sphere having electrons embedded uniformly giving an overall picture of plum pudding. (iv) The size of nucleus is measured in Fermi (1 Fermi = 10–13 cm). + – – + + Positively charged sphere – + – + + – – + Electron unifromly embedded Positive charge spreaded throughout the sphere Fig. 2.3 (v) The radius of nucleus is of the order of 1.5  10 13 cm. to 6.5  10 13 cm. i.e. 1.5 to 6.5 Fermi. Structure of atom rn  ro ( 1. 4  10 13 cm )  A 1 / 3 This exhibited that nucleus is 10 5 times small in size as compared to the total size of atom. (vi) The Volume of the nucleus is about 10 39 cm 3 and that of atom is 10 24 cm 3 , i.e., volume of the nucleus is 10 15 times that of an atom. (vii) The density of the nucleus is of the order of 10 15 g cm 3 or 10 8 tonnes cm 3 or 10 12 kg / cc. If nucleus is spherical than, Density mass of the nucleus = volume of the nucleus  mass number 4 6.023  10 23  r 3 3 (4) Drawbacks of Rutherford's model The minimum potential at which the plate photoelectric current becomes zero is called stopping potential. (3) The velocity or kinetic energy of the electron ejected depend upon the frequency of the incident radiation and is independent of its intensity. (4) The number of photoelectrons ejected is proportional to the intensity of incident radiation. (5) Einstein’s photoelectric effect equation According to Einstein, Maximum kinetic energy of the ejected electron = absorbed energy – threshold energy 1 1 1  2 mv max  h   h  0  hc    2   0   ID (i) It does not obey the Maxwell theory of electrodynamics, according to it “A small charged particle moving around an oppositely charged centre continuously loses its energy”. If an electron does so, it should also continuously lose its energy and should set up spiral motion ultimately failing into the nucleus. This phenomenon is called photoelectric effect and the electrons emitted are called photo-electrons. The current constituted by photoelectrons is known as photoelectric current. (2) The electrons are ejected only if the radiation striking the surface of the metal has at least a minimum frequency ( 0 ) called Threshold frequency. 60 following relation, E3 Generally the radius of the nucleus ( rn ) is given by the 41 D YG ST U When black body is heated, it emits thermal radiation’s of different wavelengths or frequency. To explain these radiations, max planck put forward a theory known as planck’s quantum theory. (i) The radiant energy which is emitted or absorbed by the black body is not continuous but discontinuous 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'. (ii) The energy of each quantum is directly proportional to the frequency (  ) of the radiation, i.e. E   or E  hv  threshold wavelength. Bohr’s atomic model Bohr retained the essential features of the Rutherford model of the atom. However, in order to account for the stability of the atom he introduced the concept of the stationary orbits. The Bohr postulates are, U (ii) It could not explain the line spectra of H  atom and discontinuous spectrum nature. Planck's quantum theory Where,  0 and 0 are threshold frequency and hc  Where, h  Planck's constant = 6.62×10–27 erg. sec. or 6.62  10 34 Joules sec. (iii)The total amount of energy emitted or absorbed by a body will be some whole number quanta. Hence E  nh  , where n is an integer. Photoelectric effect (1) When radiations with certain minimum frequency ( 0 ) strike the surface of a metal, the electrons are ejected from the surface of the metal. (1) An atom consists of positively charged nucleus responsible for almost the entire mass of the atom (This assumption is retention of Rutherford model). (2) The electrons revolve around the nucleus in certain permitted circular orbits of definite radii. (3) The permitted orbits are those for which the angular momentum of an electron is an intergral multiple of h / 2 where h is the Planck’s constant. If m is the mass and v is the velocity of the electron in a permitted orbit of radius r, then L  mvr  nh ; n  1 , 2, 3, ……  2 Where L is the orbital angular momentum and n is the number of orbit. The integer n is called the principal quantum number. This equation is known as the Bohr quantization postulate. (4) When electrons move in permitted discrete orbits they do not radiate or lose energy. Such orbits are called stationary or non-radiating orbits. In this manner, Bohr overcame Rutherford’s difficulty to account for the stability of the atom. Greater the distance of energy level from the nucleus, the more is 42 Structure of atom (5) Ordinarily an electron continues to move in a particular stationary state or orbit. Such a state of atom is called ground state. When energy is given to the electron it jumps to any higher energy level and is said to be in the excited state. When the electron jumps from higher to lower energy state, the energy is radiated. Advantages of Bohr’s theory (i) Bohr’s theory satisfactorily explains the spectra of species having one electron, viz. hydrogen atom, He  , Li 2  etc.  Z2 eV per atom (1eV  1.6  10 -19 J ) n2 Z2 k.cal / mole (1 cal = 4.18J) n2 1312 2 Z kJmol 1 n2 or When an electron jumps from an outer orbit (higher energy) n2 to an inner orbit (lower energy) n1 , then the energy emitted in form of radiation is given by n  Orbit number, kg , e  Charge on the 2 2 k 2 me 4 Z 2 h2  1 1  E  13. 6 Z 2  2  2  n1 n 2 As we know that E  h  , c   and   m  Mass number 1.6  10  19 electron  2 2 k 2 me 4 Z 2 ch 3 Nm 2 c 2 U 9  This can be represented as D YG After putting the values of m,e,k,h, we get. rn  n2  0.529 Å Z (iii) Calculation of velocity of electron Vn  Vn   Ze 2  2e 2 ZK , Vn    nh  mr  1/2 ; 2.188  10 8 Z cm. sec 1 n U (iv) Calculation of energy of electron in Bohr’s orbit Total energy of electron = K.E. + P.E. of electron ST kZe 2 kZe 2 kZe 2    2r r 2r Substituting of r, gives us E  2 2 mZ 2 e 4 k 2 n 2h2 Where, n=1, 2, 3……….  Putting the value of m, e, k, h,  we get E  21.8  10 12  Z2 erg per atom n2 Where, R  1   E , hc  1 1     n2  n2  2   1 Z  Atomic number of element, k = Coulombic constant 9  10  1 1    n2  n2  2   1  eV / atom   ID 9.1  10  13.6  Z2 J per atom (1 J  10 7 erg) n2 E3   n2 h2 rn   2 2 .  4  me k  Z Where, E  13.6  E  En2  En1  (ii) Calculation of radius of Bohr’s orbit : According to Bohr, radius of n th orbit in which electron moves is 31  21.8  10 19  60 the energy associated with it. The different energy levels were numbered as 1,2,3,4.. and called as K, L, M, N, …. etc.  1 1    RZ 2  2  2   n1 n 2 1     2 2 k 2 me 4 ; R is known as Rydberg ch 3 constant. Its value to be used is 109678 cm 1. The negative sign in the above equations shows that the electron and nucleus form a bound system, i.e., the electron is attracted towards the nucleus. Thus, if electron is to be taken away from the nucleus, energy has to be supplied. The energy of the electron in n  1 orbit is called the ground state energy; that in the n  2 orbit is called the first excited state energy, etc. When n   then E  0 which corresponds to ionized atom i.e., the electron and nucleus are infinitely separated H H   e  (ionization). (6) Spectral evidence for quantisation (Explanation for hydrogen spectrum on the basisof bohr atomic model) (i) The light absorbed or emitted as a result of an electron changing orbits produces characteristic absorption or emission spectra which can be recorded on the photographic plates as a series of lines, the optical spectrum of hydrogen consists of several series of lines called Lyman, Balmar, Paschen, Brackett, Pfund and Humphrey. These spectral series were named by the name of scientist who discovered them. (ii) To evaluate wavelength of various H-lines Ritz introduced the following expression, Structure of atom   1 1  1    R 2  2   c  n1 n 2  Where, R is = (vi) Thus, at least for the hydrogen atom, the Bohr theory accurately describes the origin of atomic spectral lines. 2 2me 4  Rydberg's constant ch 3 It's theoritical value = 109,737 cm–1 and 43 (7) Failure of Bohr model (i) Bohr theory was very successful in predicting and accounting the energies of line spectra of hydrogen i.e. one electron system. It could not explain the line spectra of atoms containing more than one electron. (ii) This theory could not explain the presence of It's experimental value = 109 ,677.581 cm 1 This remarkable agreement between the theoretical and experimental value was great achievment of the Bohr model. 60 multiple spectral lines. (iii) This theory could not explain the splitting of spectral lines in magnetic field (Zeeman effect) and in (iii) Although H-atom consists of only one electron yet it's spectra consist of many spectral lines. electric field (Stark effect). The intensity of these spectral lines was also not explained by the Bohr atomic model. E3 (iv) Comparative study of important spectral series of Hydrogen is shown in following table. (v) If an electron from nth excited state comes to various energy states, the maximum spectral lines n(n  1). n= principal quantum obtained will be = 2 number. As n=6 than total number of spectral lines 6(6  1) 30   15. = 2 2 ID (iv) This theory was unable to explain of dual nature of matter as explained on the basis of De broglies concept. (v) This theory could not explain uncertainty principle. (vi) No conclusion was given for the concept of quantisation of energy. Spectral series (1) (3) Lymen series Ultraviole t region n1  1 Balmer series Visible region Paschen series Infra red region Brackett series Infra red region Pfund series Infra red region Humphrey series Far infrared region ST (4) Transition U (2) Lies in the region (5) (6) n2  n1 max  D YG S.No. U Table: 2.5 Bohr–Sommerfeild’s model n1  1 and n 2  2 n 2  2,3,4....  n1  2 n 2  3,4,5....  n1 = 3 n 2  4,5,6....  n1  4 n 2  5,6,7....  n1  5 n 2  6,7,8....  n1  6 n 2  7,8....  n12n22  n12 )R (n22  max  4 3R n1  2 and n 2  3  max  36 5R n1  3 and n 2  4  max 144  7R n1  4 and n2  5 max  16  25 9R n1  5 and n 2  6  max 25  36  11 R n1  6 and n 2  7  max  36  49 13 R  min  n12 R  max n2  2 2 2  min n 2  n1 n1  1 and n 2    m in  1 R 4 3 n1  2 and n2    m in  4 R n1  3 and n 2    m in 9  R 9 5 16 7 n1  4 and n 2    m in  16 R n1  5 and n 2    min 25  R n1  6 and n 2    m in  36 R 25 9 36 11 49 13 44 Structure of atom (7) The de-Broglie equation is applicable to all material objects but it has significance only in case of microscopic particles. Since, we come across macroscopic objects in our everyday life, de-broglie relationship has no significance in everyday life. Dual nature of electron Heisenberg’s uncertainty principle (1) In 1924, the French physicist, Louis de Broglie suggested that if light has both particle and wave like nature, the similar duality must be true for matter. Thus an electron, behaves both as a material particle and as a wave. This principle states “It is impossible to specify at any given moment both the position and momentum (velocity) of an electron”. (2) This presented a new wave mechanical theory of matter. According to this theory, small particles like electrons when in motion possess wave properties. Where x  uncertainty is position of the particle, p  uncertainty in the momentum of the particle h , where h = Planck’s constant. mv h or   mc D YG Equating both  mc 2  as de-Broglie relation.  mc  p  which is same (5) This was experimentally verified by Davisson and Germer by observing diffraction effects with an electron beam. Let the electron is accelerated with a potential of V than the Kinetic energy is U 1 mv 2  eV ; m 2 v 2  2eVm 2 mv  2eVm  P ;   ST Thus 2r n nh h 2r  or mvr  2 mv n h 4 or h 4 m In terms of uncertainty in energy, E and uncertainty in time  t, this principle is written as, E. t  h 4 Schrödinger wave equation (1) Schrodinger wave equation is given by Erwin Schrödinger in 1926 and based on dual nature of electron. (2) In it electron is described as a three dimensional wave in the electric field of a positively charged nucleus. (3) The probability of finding an electron at any point around the nucleus can be determined by the help of Schrodinger wave equation which is, 2  2 y 2  2 z 2  8 2m h2 (E  V )   0 Where x, y and z are the 3 space co-ordinates, m (6) If Bohr’s theory is associated with de-Broglie’s equation then wave length of an electron can be determined in bohr’s orbit and relate it with circumference and multiply with a whole number From de-Broglie equation,   becomes, x. m v  equation x 2 h 2eVm 2r  n  or   So U energy of photon (on the basis of Einstein’s mass hc Now since p  m v x  v  (4) This can be derived as follows according to c h.c  Planck’s equation, E  h          energy relationship), E  mc 2 h 4 ID  Mathematically it is represented as , x. p  E3 (3) According to de-broglie, the wavelength associated with a particle of mass m, moving with velocity v is given by the relation 60 It is an extension of Bohr’s model. The electrons in an atom revolve around the nuclei in elliptical orbit. The circular path is a special case of ellipse. Association of elliptical orbits with circular orbit explains the fine line spectrum of atoms. = mass of electron, h = Planck’s constant, E = Total energy, V = potential energy of electron,  = amplitude of wave also called as wave function,  = for an infinitesimal change. (4) The Schrodinger wave equation can also be written as, h. mv 2   8 2m h2 (E  V )   0 Where  = laplacian operator. (5) Physical significance of  and  2 Structure of atom (i) The wave function  represents the amplitude of the electron wave. The amplitude  is thus a function of space co-ordinates and time i.e.   (x, y, z...... times ) (v) It gives the information of orbit K, L, M, N-----------. (vi) Angular momentum can also be calculated using principle quantum number (ii) For a single particle, the square of the wave probability of finding the particle at that point. (iii) If  2 is maximum than probability of finding (2) Azimuthal quantum number (l) (i) Azimuthal quantum number is also known as angular quantum number. Proposed by Sommerfield and denoted by ‘l’. 60 function ( 2 ) at any point is proportional to the e  is maximum around nucleus and the place where  probability of finding e is maximum is called electron density, electron cloud or an atomic orbital. It is (ii) It determines the number of sub shells or sublevels to which the electron belongs. (iii) It tells about the shape of subshells. different from the Bohr’s orbit. E3 (iv) It also expresses the energies of subshells (iv) The solution of this equation provides a set of number called quantum numbers which describe specific or definite energy state of the electron in atom and information about the shapes and orientations of s  p  d  f (increasing energy). (v) The value of l  (n  1) always. Where ‘n’ is the number of principle shell. (vi) the most probable distribution of electrons around the nucleus. Name of Shape of subshell U 4r2 dr 2 5 4 3 2 1 0 D YG 4r2 dr 2 4r2 dr 2 2 4 6 8 0.53Å r(Å) 1s 5 4 3 2 1 0 2 4 6 8 0.53Å 2.7Å r(Å) 2s Fig. 2.5 2 4 6 8 2.1Å r(Å) 2s U ST and s). (1) Principle quantum number (n) (i) It was proposed by Bohr and denoted by ‘n’. (ii) It determines the average distance between electron and nucleus, means it denotes the size of atom. (iii) It determine the energy of the electron in an orbit where electron is present. (iv) The maximum number of an electron in an orbit represented by this quantum number as 2n 2. No energy shell in atoms of known elements possess more than 32 electrons. 1 2 3…..(n1) = s p d f = Spher ical Dumbb ell Double Comple x dumbbe ll (vii) It represent the orbital angular momentum. h l(l  1) Which is equal to 2 (viii) The maximum number of electrons in subshell  2(2l  1) s  subshell 2 electrons d  subshell 10 electrons p  subshell 6 electrons Quantum numbers Each orbital in an atom is specified by a set of three quantum numbers (n, l, m) and each electron is designated by a set of four quantum numbers (n, l, m 0 subshell distance from nucleus as follows = ID probability is R  4r 2 dr 2. The plats of R Value of l Radial probability distribution curves : Radial 14 12 10 8 6 4 2 0 45 f  subshell 14 electrons. (ix) For a given value of ‘n’ the total values of ‘l’ is always equal to the value of ‘n’. (3) Magnetic quantum number (m) (i) It was proposed by Zeeman and denoted by ‘m’. (ii) It gives the number of permitted orientation of subshells. (iii) The value of m varies from –l to +l through zero. (iv) It tells about the splitting of spectral lines in the magnetic field i.e. this quantum number proves the Zeeman effect. (v) For a given value of ‘n’ the total value of ’m’ is equal to n 2. 46 Structure of atom (vi) For a given value of ‘l’ the total value of ‘m’ is equal to (2l  1). (vii) Degenerate orbitals : Orbitals having the same energy are known as degenerate orbitals. e.g. for p subshell p x p y p z (viii) The number of degenerate orbitals of s subshell =0. (ii) The value of ' s' is  1/2 and - 1/2, which signifies the spin or rotation or direction of electron on it’s axis during movement. (iii) The spin may be clockwise or anticlockwise. (iv) It represents the value of spin angular h momentum is equal to s(s  1). 2 (i) It was proposed by Goldshmidt & Ulen Back and denoted by the symbol of ‘s’. 60 (v) Maximum spin of an atom  1 / 2  number of (4) Spin quantum numbers (s) unpaired electron. (vi) This quantum number is not the result of solution of schrodinger equation as solved for H-atom. E3 Table : 2.6 Distribution of electrons among the quantum levels l m Designation of orbitals Number of Orbitals in the subshell 1 0 0 1s 1 2 0 0 2s 1 2 1 –1, 0, +1 2p 3 3 0 0 3s 1 3 1 –1, 0, +1 3p 3 3 2 –2, –1, 0, +1, +2 3d 5 4 0 0 4s 1 4 1 –1, 0, +1 4p 3 4 2 –2, –1, 0, +1, +2 4d 5 4 3 –3, –2, –1, 0, +1, +2, +3 4f 7 D YG U ID n Shape of orbitals (1) Shape of ‘s’ orbital U (i) For ‘s’ orbital l=0 & m=0 so ‘s’ orbital have only one unidirectional orientation i.e. the probability of finding the electrons is same in all directions. ST (ii) The size and energy of ‘s’ orbital with increasing ‘n’ will be 1s  2s  3s  4 s. (i) For ‘p’ orbital l=1, & m=+1,0,–1 means there are three ‘p’ orbitals, which is symbolised as p x , p y , p z. (ii) Shape of ‘p’ orbital is dumb bell in which the two lobes on opposite side separated by the nodal plane. (iii) p-orbital has directional properties. Z Z Z Y (iii) s-orbitals known as radial node or modal surface. But there is no radial node for 1s orbital since it is starting from the nucleus. X Px Y Y X X PY Pz Fig. 2.7 (3) Shape of ‘d’ orbital 1S Fig. 2.6 (2) Shape of ‘p’ orbitals 2S (i) For the ‘d’ orbital l =2 then the values of ‘m’ are –2, –1, 0, +1, +2. It shows that the ‘d’ orbitals has five orbitals as d xy , d yz , d zx , d x 2 y 2 , d z 2. Structure of atom (ii) Each ‘d’ orbital identical in shape, size and energy. 47 (3) Pauli’s exclusion principle (iii) The shape of d orbital is double dumb bell. According to this principle “no two electrons in an atom will have same value of all the four quantum (iv) It has directional properties. numbers”. Z Y Y X electron can have the same four quantum numbers. In other words, we cannot place two electrons with the same value of s in a 1s orbital. X dZX Z If one electron in an atom has the quantum numbers n  1 , l  0 , m  0 and s  1 / 2 , no other dXY Z 60 Z The orbital diagram does not represent a possible arrangement of 1s electrons Y Y Z X Because there are only two possible values of s, E3 X an orbital can hold not more than two electrons. dYZ (4) Hund’s Rule of maximum multiplicity dX2–Y2 Z This rule deals with the filling of electrons in the orbitals having equal energy (degenerate orbitals). Y ID According to this rule, “Electron pairing in p, d and f orbitals cannot X z2 Fig. 2.8 D YG (4) Shape of ‘f’ orbital U d occur until each orbitals of a given subshell contains one electron each or is singly occupied”. (i) For the ‘f’ orbital l=3 then the values of ‘m’ are –3, –2, –1,0,+1,+2,+3. It shows that the ‘f’ orbitals have seven orientation as fx (x 2  y 2 ) , fy(x 2  y 2 ) , fz(x 2  y 2 ), fxyz , fz 3 , fyz 2 and fxz 2. (ii) The ‘f’ orbital is complicated in shape. Rules for filling of electrons in various orbitals The atom is built up by filling electrons in various orbitals according to the following rules, U (1) Aufbau’s principle ST This principle states that the electrons are added one by one to the various orbitals in order of their increasing energy starting with the orbital of lowest energy. The increasing order of energy of various orbitals is 1s  2 s  2 p  3 s  3 p  4 s  3 d  4 p  5 s  4 d  5 p  6 s  4 f  5d  6 p  7 s  5 f  6d  7 p......... (2) (n+l) Rule In neutral isolated atom, the lower the value of (n + l) for an orbital, lower is its energy. However, if the two different types of orbitals have the same value of (n + l), the orbitals with lower value of n has lower This is due to the fact that electrons being identical in charge, repel each other when present in the same orbital. This repulsion can however be minimised if two electrons move as far apart as possible by occupying different degenerate orbitals. All the unpaired electrons in a degenerate set of orbitals will have same spin. As we now know the Hund’s rule, let us see how the three electrons are arranged in p orbitals. The important point ot be remembered is that all the singly occupied orbitals should have electrons with parallel spins i.e in the same direction either-clockwise or anticlockwise. 2px 2py 2pz 2px 2py 2pz or Electronic configurations of elements On the basis of the elecronic configuration principles the electronic configuration of various elements are given in the following table : The above method of writing the electronic configurations is quite cumbersome. Hence, usually the electronic configuration of the atom of any element is simply represented by the notation. energy. number of principal shell nlx Number of electrons Present symbol of subshell 48 Structure of atom  The d orbital which does not have four lobes is dz 2  The d orbital whose lobes lie along the axis is Some of the exceptions are important though, because they occur with common elements, notably chromium and copper. Cu has 29 electrons. Its excepted electronic configuration is 1s 2 2 s 2 2 p 6 3 s 2 3 p 6 4 s 2 3d 9 but in reality the configuration is 1s 2 2 s 2 2 p 6 3 s 2 3 p 6 4 s1 3d 10 as this configuration is more stable. Similarly Cr has the of 1s 2 2 s 2 sp 6 3 s 2 3 p 6 4 s 1 3d 5 instead of  Spin angular momentum  s(s  1) n 2  Magnetic Factors responsible for the extra stability of halffilled and completely filled subshells, magnetron) of n unpaired e (Bohr  Exception of E.C. are f orbital will be Cr (24 ) , Cu (29 ) , Mo (42 ) , Ag (47 ) , W (74 ) , Au (79 ).  No. of waves n  2r   No. of revolutions of (where   h ) mv e  per second is  v. 2r  The solution of schrodinger wave equation gives principal, azimuthal and magnetic quantum numbers but not the spin quantum number.  In the Rydberg formula, when n 2   the line U D YG U (ii) Exchange energy : The electrons with parallel spins present in the degenerate orbitals tend to exchange their position. The energy released during this exchange is called exchange energy. The number of exchanges that can take place is maximum when the degenerate orbtials (orbitals of same subshell having equal energy) are exactly half-filled or completely. As a result, the exchange energy is maximum and so it the stability. B.M. e   Ion with unpaired electron in d or ID (i) Symmetrical distribution : It is well known fact that symmetry leads to stability. Thus the electronic configuration in which all the orbitals of the same subshell are either completely filled or are exactly half filled are more stable because of symmetrical distribution of electrons.  n(n  2) moment coloured. 1s 2 2 s 2 2 p 6 3 s 2 3 p 6 4 s 2 3 d 4. h 2  Total spin   ; where n is no of unpaired E3 configuration d x 2 y 2 60 Some Unexpected Electronic Configuration  All lines in the visible region are of Balmer series ST but reverse is not true i.e., all Balmer lines will not fall in visible region.  A part of an atom up to penultimate shell is a kernel or atomic core.  If the energy supplied to hydrogen atom is less than 13.6 eV it will awpt or absorb only those quanta which can take it to a certain higher energy level i.e., all those photons having energy less than or more than a particular energy level will not be absorbed by hydrogen atom, but if energy supplied to hydrogen atom is more than 13.6eV then all photons are absorbed and excess energy appear as kinetic energy of emitted photo electron.  No of nodes in any orbital  (n  l  1)  No of nodal planes in an orbitals  l produced is called the limiting line of that series.  Among various forms of visible light, violet colour has shortest wavelength, highest frequency and highest energy.  Red coloured light has largest wavelength, least frequency and lowest energy in visible light.  Elements give line spectra. The line spectrum is characteristic of the excited atom producing it. No two elements have identical line spectrum.  The line spectrum results from the emission of radiations from the atoms of the elements and is therefore called as atomic spectrum.  Atoms give line spectra (known as atomic spectrum) and the molecules give band spectra (known as molecular spectrum).  The negative potential at which the photoelectric current becomes zero is called cut off potential or stopping potential.  When energy or frequency of scattered ray is lesser than the incident ray, it is known as Compton effect.  The instrument used to record solar spectrum is called spectrometer or spectrograph developed by Bunsen and Kirchoff in 1859.  The intensities of spectral lines decreases with Structure of atom 49 [IIT 1982; BITS 1988;CPMT 1977; NCERT 1974; increase in the value of n. For example, the intensity of first Lyman line (2 1) is greater than second line MP PMT 1992; MP PET 2002] (3 1) and so on. (a) James Chadwick (b) William Crooks  In Balmer series of hydrogen spectrum the first (c) J.J. Thomson (d) Rutherford is called limiting line. Discovery and Properties of anode, cathode rays neutron and Nuclear structure 1. A neutral atom (Atomic no. > 1) consists of [CPMT 1982] (b) Neutrons + protons (c) Neutrons + electrons The nucleus of the atom consists of [CPMT 1973, 74, 78, 83, 84; MADT Bihar 1980; D YG DPMT 1982, 85; MP PMT 1999] (a) Proton and neutron (b) Proton and electron (c) Neutron and electron (d) Proton, neutron and electron 3. The size of nucleus is of the order of [CPMT 1982; MP PMT 1991] (a) 10 12 m (d) 10 10 m Positive ions are formed from the neutral atom by the ST 4. (b) 10 8 m U (c) 10 15 m [CPMT 1976] (a) Increase of nuclear charge (b) Gain of protons (c) Loss of electrons (d) Loss of protons 5. The electron is [DPMT 1982; MADT Bihar 1980] 6. (a)  -ray particle (b)  -ray particle (c) Hydrogen ion (d) Positron Who discovered neutron [BHU 2005] (a) Proton (b) Electron (c) Neutron (d) Alpha U (d) Neutron + proton + electron 2. The ratio of charge and mass would be greater for ID (a) Only protons 7. 60 (4 2) is L  line. The line from infinity energy shell E3 line (3 2) is also known as L line. The second line