Atomic Structure Notes

Page # 1 ATOMIC STRUCTURE ATOMIC STRUCTURE 1. INTRODUCTION (a) The word atom was first introduced by Ostwald (1803 - 1807) in scientific world. (b) According to him matter is ultimately made up of extremely small indivisible particles called atoms. (c) It takes part in chemical reactions. (d) Atom is neither created nor destroyed (c) The molar mass of electron is 5.48×10–4 gm/mole 2. DALTON’S ATOMIC THEORY Dalton proposed the atomic theory on the basis of the law of conservation of mass and law of definite proportions. He also proposed the law of multiple proportion as a logical consequence of this theory. The salient features of this theory are (a) Each element is composed by extremely small particles called atoms. (b) Atoms of a particular element are all alike but differ with the atoms of other elements. (c) Atom of each element is an ultimate particle, and has a characterist ic mass but i s structureless. (d) Atom is indestructible i.e. it can neither be destroyed nor created by simple chemical reactions. (e) Atom of an element takes part in chemical reaction to form molecule. (f) In a given compound, the relative number and kind of atom are same. (g) Atoms of different elements combine in fixed ratio of small whole numbers to form compound atoms (now called molecules). 2.1 Merits and Demerits of Dalton’s theory : 2.1.1 Merits : (a) Dal ton’s theory expla ins the l aw of conservation of mass and some other laws of chemical combination. (b) Atoms of elements take part in chemical reaction is true till today. 2.1.2 Demerits : (a) There is no mention of atomic weights of elements. (b) He could not explain that why do atoms of same element combined with each other. (c) The law of definite proportion fails if different isotopes are used. where m’ = mass of the electron in motion m = rest mass, v = velocity of the electron c = velocity of light (e) In 1897, J.J. Thomson determined the e/m value (charge/mass) of the electron by studying the deflections of cathode rays in electric and magnetic fields. The value of e/m has been found to be –1.7588 × 108 coulomb (f) The first precise measurement of the charge on the electron was made by Robert A. Millikan. in 1909 by oil drop experiment. Its value was found to be - 1.6022 x 10–19 coulomb. (g) The mass of electron can be calculated from the value of e/m and the value of e which is 9.1096 × 10–31 Kg. 3.1.1 Cathode rays 3. FUNDAMENTAL PARTICLES 3.1 Properties of electron (a) Electron was discovered by Sir J.J. Thomson (b) The charge on the electron is 1.6 × 10–19 coulomb/gm (Millikan) 1 (d) The mass of electron in motion is expressed as m´ = m F1 – v I GH c JK 2 ½ 2 Gas at low pressure Cathode rays To vacuum pump Anode + Cathode - - + High voltage (a) The electron was discovered as a result of the studies of the passage of electricity through gases at extremely low pressures known as discharge tube experiments. (b) When a high voltage of the order of 10,000 volts or more was i mpressed across the electrodes, some sort of invisible rays moved from the negative electrode to the positive electrodes these rays are called as cathode rays (c) Cathode rays have the following properties. (i) Path of travelling is straight from the cathode with a very high velocity As it produces shadow of an object placed in its path Page # 2 ATOMIC STRUCTURE Object To vacuum pump Shadow - + ZnS screen + - (ii) Cathode rays produce mechanical effects. If a small pedal wheel is placed between the electrodes, it rotates. This indicates that the cathode rays consist of material part To vacuum pump - + Light mica wheel mounted on axis - (c) Mass of proton is 1.672 x 10–27 kg or 1.0072 amu (d) A proton is defined as a sub-atomic particle which has a mass nearly 1 amu and a charge of +1 unit 3.2.1 Positive Rays-Discovery of Proton (a) The existence of positively charged particles in an atom was shown by E. Goldstein in 1886 (b) He repeated the same discharge tube experiments by using a perforated cathode. (c) It was observed that when a high potential difference was applied between the electrodes, not only cathode rays were produced but also a new type of rays were produced simultaneously from anode moving towards cathode and passed through the holes or canal of the cathode. These termed as canal ray or cathode ray Perforated cathode Railing + (iii) When electric and magnetic fields are applied to the cathode rays in the discharge tube, the rays are deflected thus establishing that they consist of charged particles. Wall coated with ZnS + + - Low voltage 10 volts Anode with High voltage a hole (10, 000 volts) (iv) Cathode rays produce X-rays when they strike against hard metals like tungsten, copper etc. (v) When the cathode rays are allowed to strike a thin metal foil, it gets heated up. Thus the cathode rays possess heating effect. (vi) They produce a green glow when strike the glass wall beyond the anode. Light is emitted when they strike the zinc sulphide screen. (vii) Cathode rays penetrate. Through thin sheets of aluminium and other metals. (viii) They affect the photographic plates (ix) The ratio of charge to mass i.e. charge/ mass is sam e for al l the ca thod e rays irrespective of the gas used in the tube. 3.2 Properties of proton (a) Proton was discovered by Goldestein (b) Proton carries a charge of +1.602 x 10–19 coulomb, i.e., one unit positive charge. + Cathode ray Positive rays Cathode (d) Characteristics of Anode Rays are as follows. (i) These rays travel in straight lines and cast shadow of the object placed in their path. (ii) The anode rays are deflected by the magnetic and electric fields like cathode rays but direction is different that mean these rays are positively charged. (iii) These rays have kinetic energy and produces heating effect also. (iv) The e/m ratio of for these rays is smaller than that of electrons (v) Unlike cathode rays, their e/m value is dependent upon the nature of the gas taken in the tube. (vi) These rays produce flashes of light on Zn-S screen (vii) These rays can pass through thin metal foils (viii)They are capable to produce ionisation in gases (ix) They can produce physical and chemical changes. 3.3 Properties of neutron (a) This was discovered 20 years after the structure of atom was elucidated by Rutherford. (b) It has been found that for all atoms except hydrogen atomic mass is more than the atomic number. Thus Rutherford (1920) suggested that in an atom, there must be present at least a Page # 3 ATOMIC STRUCTURE third type of fundamental particle. (c) It should be electrically neutral and posses mass nearly equal to that of proton. He proposed its name as neutron. (d) Chadwick (1932), bombarded beryllium with a stream of -particles and observed electrically and magnetically neutral radiations. (e) There were neutral particles which was called neutron. Nuclear reaction is as follows 9 + 4 12 + 1 4Be 2He  6C 0n (f) A neutron is a subatomic particle which has a mass 1.675 x 10–24g, approximately 1 amu, or nearly equal to the mass of proton on hydrogen atom and carrying no electrical charge. 4. NON FUNDAMENTAL PARTICLES 4.1 Positron : (a) It is also called positive electron and symbolised as 1e0 or e+. (b) It was discovered by ANDERSON in 1932. (c) It is the positive counterpart of electron. (d) Mass of positron is same as electron m = 9.1 × 10–28g. (e) Charge of positron is same but opposite signed as electron e = –1.6 × 10–19 C. (f) It is very unstable and combines with electron producing  rays. 4.2Neutrino and Antineutrino : These are particles of approximately zero masses and zero charge. 4.3 Antiproton : (a) It was discovered by Seagre. (b) Mass of this particle is equal to 1.673 × 10–24 g. (c) Charge of Antiproton is –1.6 × 10–19 C. 4.4 Meson () : (a) It was discovered by Yukawa in 1935. (b) It may possess 3 types of charges. (c) On the Basis of charge, the meson is of three types, -meson, µ-meson and neutral meson (º). (d) -mesons are called pions. (e) It tells about the stability of nucleus. (f) The mass of this particle is 200 times of electron i.e. It is heavier than electron but lighter than proton. 5. THOMSON’S MODEL It states the arrangement of electrons and protons in an atom. The main principles are (a) After discovery of electron and proton attempts were made to find out their arrangement in an atom. The first simple model was proposed by J.J. Thomson known as Thomson’s atomic model. (b) He proposed that the positive charge is spread over a sphere of the size of the atom (i.e. 10–8 cm radius) in which electrons are embedded to make the atom as whole neutral. (c) This model could not explain the experimental results of Rutherfords -particle scattering, therefore it was rejected. 6. RUTHERFORD’S MODEL Rutherford carried out experiment on the bombardment of atoms by high speed positively charged  - particles emitted from radium and gave the following observations, which was based on his experiment. Radioactive substance Very few Thin gold Few Most Lead block Lead plate with hole Few (a) Most of the  - particles (nearly 99%) continued with their straight path. (b) Some of the  - particles passed very close to the centre of the atom and deflected by small angles. (c) Very few particles thrown back (180º). Atom of metal foil Few Beam of –particles  Majority of –rays Very Few Atom of metal foil Majority of –rays Few 6.1 Main features : (a) Most of the  - particles were continued their straight path that means most of the space of the atom is empty. (b) The centre of an atom has a positively charged body called nucleus which repel positively charged  - particles and thus explained the scattering phenomenon. (c) Whole mass of an atom is concentrated in its nucleus and very few throw back means the size of the nucleus is very small 10–13 cm. It showed that the nucleus is 10–5 times small in size as compared to the total size of atom. (d) The size and volume of the nucleus is very small as compared to the total size and volume of atom. (e) As atomic number increases, the angle of deflection () increases. Page # 4 ATOMIC STRUCTURE 6.2 Drawbacks of Rutherford’s model : (a) According to classical electromagnetic theory, when an electron moves around the nucleus under the influence of the attractive force, the electron loses its energy continuously and move closer and closer to the nucleus in a spiral path, the ultimate result will be that it will fall into the nucleus but it can’t be possible because an atom is quite stable. (b) If an electron loses energy continuously, the observed spectrum should be continuous but the actual observed spectrum consist of discontinuous well defined lines of definite frequencies. 7. MOSELEY’S EXPERIMENT 7.1 Atomic number (Z) : The number of positive charge carried by the nucleus of an atom is termed as atomic no. (Z) or the number of protons in an atom of an element is equal to its atomic number. Since an atom is electrically neutral it contains an equal number of extra nuclear electrons. Thus – Atomic No. = Number of unit positive charge in nucleus = Number of protons = Number of electrons. 7.2 Mass number or Neucleon number (A) : The mass number being the sum of the number of protons and neutrons in the nucleus, which is always a whole number. A = P + n or A = Z + n where : A = Mass number P = Number of protons n = Number of neutrons Z = Atomic number On the another side of that statement since mass of a proton or a neutron is not a whole number (on atomic weight scale), atomic weight is not necessarily a whole number. For example : The isotopes of oxygen having mass number 17 and 18, have atomic weights equal to 17.00045 and 18.0037 respectively. 8. BOHR’S ATOMIC MODEL Bohr developed atomic model for hydrogen and hydrogen like one electron species on the basis of Planck’s quntum theory. 8.1 The important postulates of Bohr model of an atom : 4 or N 3 or M 2 or L Nucleus (a) Electron revolves around the nucleus in a fixed circular orbit of definite energy. (b) Electron revolves only in those orbits whose angular momentum (mvr) is an integral multiple of the factor h/2  (where ‘h’ is Planck’s constant) mvr = n h 2 where : m = mass of the electron v = velocity of the electron n = number of orbit in which electron revolves i.e. n = 1, 2, 3 ......... r = radius of the orbit. (c) As long as the electron occupy a definite energy level, it does not radiate out energy i.e. it does not lose or gain energy. (d) The energy is emitted or absorbed only when the electron jumps from one energy level to another. If energy is supplied to an electron, It may jump higher energy level to the lower by the emission of energy. This higher energy level called excited state. Similarly in the reverse process it may absorb energy and jump from lower to higher energy level. This amount of energy emitted or absorbed is given by the difference of the energies of the two energy levels concerned. n = 2 ————— E2  E = E2 – E1  n = 1 ————— E1 n = 2 ————— E2 Absorbed energy  E = E1 – E2        n = 1 ————— E1 Emitted energy 8.2 Mathematical term of Bohr’s Postulates : 8.2.1 Calculation of the radius of the Bohr’s orbit: Suppose that an electron having mass ‘m’ and charge ‘e’ revolving around the nucleus of charge ‘Ze’ (Z is atomic number & e = charge) with a tangential / linear velocity of ‘v’. Further Page # 5 ATOMIC STRUCTURE consider that ‘r’ is the radius of the orbit in which electron is revolving. According to Coulomb’s law, the electrostatic force of attraction (F) between the moving electron and nucleus is - KZe 2 F = Where : K = constant = r2 mv 2 and the centrifugal force F = r For the stable orbit of an electron both the forces are balanced, v2 = n 2h 2 = In C.G.S.  r 2Ze 2 nh on purtting the values of  e– and h v  2.188  10 8  n 2h 2 4 2mKZe 2 1 n 8.2.3 Calculation of energy of an electron : The total energy of an electron revolving in a particular orbit is T. E. = K. E. + P. E. Where ; P. E. = Potential energy, K.E. = Kinetic energy, T.E.= Total energy 1 The K.E. of an electron = mv2 2 and the P.E. of an electron = – unit K  1, 42 Ze2 h = 6.62 × 10–27 erg. sec. m = 9.1 × 10–28 g e = 1.6 × 10–19 C. on putting the value or e, h, m then n2 Å Z Hence, T.E. = 1 KZe 2 mv2 – 2 r We know that, KZe 2 mv 2 = r r2 KZe 2 r KZe 2 r substituting the value of mv2 in the above equation : KZe 2 KZe 2 KZe 2 T.E.= – = – 2r r 2r or mv2 = KZe 2 2r 0In C.G.S. unit K = 1 r  n2 So, 1 Z Orbital frequency Z cm / sec n vZ where ; r 2mn 2h 2 v n 2h 2 r  0.529  nh  4  2mZe 2 v From equation (1) and (2) : on solving, we will get r v = …(1) …(2) 4 2m 2r 2 nh nh v = 2 2mr To keep the value of ‘r’ on the equation (1) mvr = then 1 = 9 × 109 Nm2/C2 4  0 KZe 2 mv 2 i. e. at equilibrium = r r2 KZe 2 then V2 = mr From the postulate of Bohr, nh mvr = 2 nh v = 2mr 8.2.2 Calculation of velocity of an electron in Bohr’s orbit : Velocity of the revolving electron in nth orbit is given by – v 2r f = 1 T.E. = – Ze 2 2r Substituting the value of ‘r’ in the equation of T.E. .  T.E. = – Page # 6 ATOMIC STRUCTURE Then, 4  2 Ze 2m 2 2 Z 2 e 4 m Ze2 – × = 2r n 2h2 n 2h 2 Thus, the total energy of an electron in nth orbit is given by E =  En = – 2 2 2 8.2.4 Relation between P. E., K. E. & T. E. : Ze 2 1 Ze 2 P. E. = – , K. E. = , r 2 r 1 Ze 2 T. E. = – 2 r 1 Ze 2 r Ze 2 – r 1 2 = …(1) 1 Ze 2 2 r 1 Ze 2 2 r – T . E. = – K. E. …(2) P.E.  –K.E. 2 …(3) T.E.  (a) T. E. = – 13.6 × Z2 eV / atom n2 (b) T. E. = – 21.8 × 10–19 × (c) T. E. = – 21.8 × 10–12 × (d) T. E. = – 313.6 × Z Z2 n2 Z2 n2 J / atom erg / atom 2 n2 Kcal / mole (a) The negative sign of energy indicates that there is attraction between the negatively 2 hv = 2 4 2 2 1 2 2mZ 2 e 4 n12h2 2 2mZ 2 e 4 – LM MN 2 2me 4  ch 3  n 22h2 1 1 2 2mZ 2 e 4 hc = × 2 – 2 2 n n  h 1 2 v = c  OP PQ Rydberg constant LM MN OP PQ 1 1 1 = RHZ2 2 – 2 where  n1 n2 m = 9.1 × 10–28 gram by the theoretical value of RH = 109737 / cm e = 4.8 × 10–10 e.s.u. by the practical value of RH = 109677 / cm c = 3 × 1010 cm/sec by the calculative value of RH = 109700 / cm h = 6.625 × 10–27 erg-sec Rydberg constang for other atom R = RH x Z2  = 9. ELECTROMAGNETIC RADIATIONS Light and other forms of radiant energy propagate without any medium in the space in the form of waves. These waves can be produced by a charged body moving in a magnetic field or a magnet in an electric field. e.g.  - rays,  - rays, Cosmic rays, Ordinary light rays etc. 9.1 Characteristics radiations: Z Y ield ic f ctr Ele 8.2.5 Conclusions from equation of energy : 2 4 2 2 2 Then, Then T. E. = ½ P. E. Then hv = RH = 2 – T.E. = P.E. T.E. = K.E. LM –2 mZ e OP LM –2 mZ e OP MN n h PQ – MN n h PQ 2 2 Z 2 e 4 m n h Note : – The P.E. at the infinite = 0 The K.E. at the infinite = 0 So, 8.3 Calculation of Rydberg Constant Suppose that an electron transist from first energy level to second energy level. Then, the change of energy is given by  E = E2 – E1 hv = E 2 – E1 of electromagnetic Direction of propagation X charged electron and positively charged nucleus. equation are constant for an element except ‘n’ which is an integer such as 1, 2, 3 etc. i. e. the energy of an electron is constant as long as the value of ‘n’ is kept constant. (c) The energy of an electron is directly proportional to the square of ‘n’. µ s (b) All the quantities of R.H.S. in the energy (a) All electromagnetic waves move or travel with the same velocity equal to that of light. (b) They do not req uire any medium to propagate. (c) These consist of electric and magnetic field Page # 7 ATOMIC STRUCTURE that oscillate in the direction perpendicular to each other and to the direction in which the wave is propagate. 9.2 Some Important characteristics of electromagnetic waves : (a) Frequency () : It is defined as the no. of waves which pass through a given point in per sec. It’s unit is expressed by cycle per second (cps) or Hertz (Hz).  c  c  (c) Wave No. ( v ) : It is defined as the number of wave per cm and it is equal to the inverse of wavelength. Its unit is cm–1. v= 1  v = c = cv  (d) Amplitude (a) : It denotes the height of the crest or depth of the trough of a wave. It determines the intensity of brightness of radiation. (e) Velocity (v) : The distance traveled per sec by a wave called velocity of a wave. It is expressed by the unit of m/sec. or cm/sec. 10. SOLAR SPECTRUM Red Slit Orange Prism Discharge tube containing hydrogen ‘ Name Screen Yellow Green Blue Indigo Violet Line spectrum (a) When sunlight is passed through a prism, It absorbs wavelength range of black colour radiation and other splits into a series of colour bands known as emission spectrum and black colour band which is known as absorption spectrum.  in Å Radio waves 3×109 toby 3×10 14 Microwaves Note : A cycle is said to be completed when a wave consisting of crest and trough passes through a point. (b) Wavelength ( ) : The distance between two adjacent crest or troughs of the wave as shown in the fig. It is denoted by lambda ( ) a greek letter and unit is Angstrom (Å) or nanometer (nm). 1 Å = 10–10 m or 10– 8 cm – 9 1 nm = 10 m or 10– 7 cm  (b) The splitting of light into seven colours is called emission Spectrum. (c) The characteristic range of wavelength of el ectromagneti c radi ation situated in an increasi ng or d ecreasing order cal l ed electromagnetic spectrum. I.R. 3 × 106 to 3 × 109 7600×3×106 Origin the Alternating current of high frequency by the generator of high quality from the heated things Visiblewave U.V. wave 3800 to7600 150 to from the sun rays 3800 X-rays 0.1 to 150 to put a metallic barrior in path of moving electron rays 0.01 to 0.1 by radio active disintegration Cosmic rays 0 to 0.01 from the outer most part of sun  decreases Increases (d) Band spectrum is originated by molecules and linear spectrum is originated by atoms. 10.1 Difference between absorption spectra : Emission spectrum 1.It is obtained when radiation emitted by the excited substance which is analysed in a spectroscope 2.This type of spectrum lines consist of bright coloured lines separated by dark spaces. Emission and Absorption spectrum It is obtained when white light is passed through the substance either gases or in the form of solution. It is consist of dark on a colour back ground. 11.ATOMIC SPECTRA OR LINE SPECTRA Atomic spectra is line spectra. So atomic spectrum is also called line spectrum. It is of two types 11.1 Emission spectrum : A substance gets excited on heating at a very high temperature or by giving energy and radiations are emitted. These radiations when analysed with the help of spectroscope, spectral lines are obtained. A substance may be excited as follows - Page # 8 ATOMIC STRUCTURE (a) By heating at a higher temperature. (b) By passing electric current at a very low pressure in a discharge tube filled with gas. (c) By passing electric current into metallic filament. Emission spectra is of two types (i) Continuous spectrum (ii) Line spectrum (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 is resolved through prism or spectroscope, it also gives continuous spectrum of colours. (ii) Line spectrum : If the radiations obtained by the excitation of a substance are analysed with the 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. For example on heating sodium chloride or any other salt of sodium in Bunsen flame bright yellow light is emitted. The emitted light when viewed through a spectroscope two isolated yell ow lines separated by dark space are obtained. The wave lengths of these lines are 5890Å and 5896Å. If an electron from nth excited state comes to various energy states, the maximum spectral lines obtained will be n( n  1) = 2 11.2 Absorption spectrum When the white light of an incandescent substance i s pa ssed through any oth er substance, this substance absorbs the radiations of certain wavelength from the white light. On analysing the transmitted light we obtain a spectrum in which dark lines of specific wave lengths are observed. These lines constitute the absorption spectrum. The wave length of the dark lines correspond to the wavelength of light absorbed. 12. HYDROGEN SPECTRUM (a) Hydrogen spectrum is an example of line emission spectrum or atomic emission spectrum. (b) When an electric discharge is passed through hydrogen gas at low pressure, a bluish light is emitted. (c) This light shows discontinuous line spectrum of several isolated sharp lines through prism. (d) All thes lines of H-spectrum have following six series Spectral series Wavelength region Lyman U.V. Balmer Visible Paschen R Brackett R Pfund R Humphrey Far .R. These spectral series were named by the name of scientist who discovered them (e) To evaluate wavelength of various H-lines Ritz introduced the following expression  = 1  = = R  C LM 1  1 OP Nn n Q 2 1 2 2 Where R is a universal constant known as Rydberg’s constant its value is 109, 678cm–1. (f) Although H - atom consists only one electron yet it’s spectra consist of many spectral lines. LM N 1 1 1  v  RH 2  2  n1 n 2 OP Q 12.1 Lyman Series (a) It is a first series of spectral series of H. (b) It was found out in ultraviolet region in 1898 by Lyman. (c) It’s value of n1 = 1 and n2 = 2, 3, 4 where ‘n1’ is ground state and ‘n2’ is called excited state of electron present in a H - atom. (d) If the electron goes to n1 = 1 to n2 = 2 — first Lyman series If the electron goes to n1 = 1 to n2 = 3 — Second Lyman series If the electron goes to n1 = 1 to n2 = 4 — third Lyman series ----- so on. (e) LM N 1 1 1  RH 2  2  1 n2 OP Q where n2 > 1 always. n12 (f) The wavelength of marginal line = for RH 1 all series. So, for lyman series = RH 12.2 Balmer series : (a) It is the second series of H-spectral series. (b) It was found out in 1892 in visible region by Balmer. (c) Balmer series was found out before all series. Because it was found to be in visible region. (d) It’s value of n1 = 2 and n2 = 3, 4, 5 ........... where n1 is ground state and n2 is excited state. (e) If the electron goes to n1 = 2 to n2 = 3 — First Balmer series If the electron goes to n1 = 2 to n2 = 4 — Second Balmer series Page # 9 ATOMIC STRUCTURE If the electron goes to n1 = 2 to n2 = 5 — third Balmer series .... so on (f) The wavelength of marginal line of Balmer 2 n1 22 4   series = RH RH RH (g) F GH 1 1 1  RH 2  2  2 n2 I JK where n2 > 2 always 12.3 Paschen series : (a) It is the third series of H - spectrum. (b) It was found out in infra red region by Paschen. (c) It’s value of n 1 = 3 and n 2 = 4, 5, 6 ............ where n1 is ground state and n2 is excited state. (d) If the electron goes to n1 = 3 to n2 = 4 — First paschen series If the electron goes to n1 = 3 to n2 = 5 — second paschen series If the electron goes to n1 = 3 to n2 = 6 — third paschen series ------ so on. (e) The wavelength of marginal line of paschen 2 n1 32 9   series = . RH RH RH (f) LM N 1 1 1  RH 2  2  3 n2 OP Q where n2 > 3 always. 12.4 Brackett series : (a) It is fourth series of H - spectrum. (b) It was found out in infra red region by Brackett. (c) It’s value of n 1 = 4 and n 2 = 5, 6, 7 ................ where n1 is ground state and n2 is excited state. (d) If the electron goes to n1 = 4 to n2 = 5 — first brackett series If the electron goes to n1 = 4 to n2 = 6 — second brackett series If the electron goes to n1 = 4 to n2 = 7 — third brackett series ------ so on. (e) The wavelength of marginal line of brackett n12 42 16   series = RH RH RH (f) LM N 1 1 1  RH 2  2  4 n2 OP Q Where n2 > 4 always. 12.5 Pfund series : (a) It is fifth series of H - spectrum. (b) It was found out in infra red region by Pfund. 1 (c) It’s value of n1 = 5 and n2 = 6, 7, 8 ............... where n1 is ground state and n2 is excited state. (d) If the electron goes to n1 = 5 to n2 = 6 — first Pfund series If the electron goes to n1 = 5 to n2 = 7 — second Pfund series If the electron goes to n1 = 5 to n2 = 8 — third Pfund series -----so on. (e) The wavelength of marginal line of Pfund n12 52 25   series = RH RH RH (f) LM N 1 1 1  RH 2  2  5 n2 OP Q where n2 > 5 always. 12.6 Humfrey series : (a) It is the sixth series of H - spectrum. (b) It was found out in infra-red region by Humfrey. (c) It’s value of n1 = 6 and n2 = 7, 8, 9 ------- where n1 is ground state of electron and n2 is excited state. (d) If the electron goes to n1 = 6 to n2 = 7 — first Humfri series If the electron goes to n1 = 6 to n2 = 8 — second Humfri series If the electron goes to n1 = 6 to n2 = 9 — third Humfri series .. so on. (e) The wavelength of marginal line of Humfri n12 62 36   RH RH RH series = LM MN 1 1 1 (f)   RH 2  2 6 n2 OP PQ where n2 > 6. 13. CONCEPT OF QUANTIZATION (a) E.M. wave theory successfully explains about reflection, refraction, diffraction, etc. but it fails to explain black body radiations and photo electric effect (b) To explain all these things Max planck gave a new revolutionary theory in 1901, called as quantum theory of radiation. (c) According to this theory, a hot body emits radiant en ergy not contin uously but discontinuously in the form of small packets of energy called quantum. (d) In case of light, the quantum of energy is often called photon. (e) The amount of energy associated with a quantum radi ation is proportional to the frequency of light E   or E = h Page # 10 ATOMIC STRUCTURE where the proportionality constant, h is a universal constant known as Planck’s constant. Its value is 6.63 × 10–34 J-sec (f) The total amount of energy emitted or absorbed by a body will be some whole number multiple of quantum, i.e. E = nh where n is an integer such as 1, 2, 3 ...... 14. FAILURES/LIMITATIONS OF BOHR’S THEORY (a) He could not explain the line spectra of atoms containing more than one electron. (b) He also could not explain the presence of multiple spectral lines. (c) He was unable to explain the splitting of spectral lines in magnetic field (Zeeman effect) and in electric field (Stark effect). (d) No one conclusion was given for the principle of quantisation of angular momentum. (e) He was unable to explain the de-Broglie’s concept of dual nature of matter. (f) He coul d not explai n Heisenberg’s uncertainty principle. 15. SOMMERFELD’S CONCEPT Extension of Bohr’s theory (a) Sommerfeld in 1915, introduced a new atomic model to explain fine spectrum of hydrogen atom (b) He proposed that the moving electron might describe elliptical orbits in addition to circular, orbits and the nucleus is situated at one of the foci. (c) During motion on a circle, only the angle of revolution changes while the distance from the nucleus remains the same but in elliptical motion both the angle of revolution and the distance of the electron from the nucleus change. (d) The distance from the nucleus is termed as radius vector and the angle of revolution is known as azimuthal angle. (e) The tangential velocity of the electron at a particular instant can be resolved into two components. One along the radius vector called radial velocity and the other perpendicular to the radius vector called transverse or angular velocity. (f) These two velocities give rise to radial momentum and angular or azimuthal momentum. 1 (g) Sommerfeld proposed that both the momenta must be integral multiples, radial momentum h = nr h , Azimuthal momentum = n 2  2 The brief explanations of Sommerfeld’s model are as follows (i) Sommerfield model gives introduction of elliptical orbitals. (ii) Bohr’s circular orbit has considered to be a special case of an elliptical orbit, in which the length of major and minor axis is same. (iii) Only one co-ordinate angle of revolution  is variable in circular orbit but in elliptical, vector radius ‘r’ is also variable. (iv) Introduction of azimuthal quantum number in addition to the principal quantum number. Angular momentum of an electron moving around elliptical orbit is the sum of two vector terms as follows = change  = change r = change r = constant n h n h P = Pr + P  = r  n = nr + n 2 2 Where, n = Principal quantum number nr = Radial quantum number = 1, 2, 3, ..............  n= Azimuthal quantum number = 1, 2, 3, ............... n (v) Introduction of sub shells or sub energy levels within principal energy levels. These were considered to had different energies. (vi) Sub shell are termed as s, p, d, f (sharp, principal, diffused, fundamental). (vii) These subshells were considered to had capacity of 2, 6, 10, 14 electrons respectively. (viii)Energies of these subshells follow the order s < p < d < f. (ix) The relation between principal (n) and azimuthal () quantum number is - length of major axis n = length of min or axis  (x) The subshells (s, p, d, f) in principal energy level have very slight difference in their energies. The spectral lines corresponding to the transition of electron in their sublevels have a fine structure. This was major achievement of this extension. (xi) First energy level (K or n = 1) of Bohr contains only one subshell (s). Second (L or n = 2) contains two subshell (s & p). Third (M or n = 3) contains three subshell (s, p and d). Fourth (N or n = 4) contains four subshell (s, p, d, f). Page # 11 ATOMIC STRUCTURE (According to Sommerfield, nth shell of Bohr has n subshell in which one circular & (n – 1) elliptical subshells are present.) The necessity of a modification of the Bohr theory stemmed from the spectral observation, under high resolution of the different hydrogen lines. Extending Bohr’s ideas sommerfeld suggested that If a and b are semimajor and semiminor axes. b k k It follows a  k  n  n r 16. WAVE MECHANICAL MODEL OF ATOM 16.1 Dual nature of electron (a) Einstein had suggested that light can behave as a wave as well as like a particle i.e. it has dual character (b) In 1924, de-Broglie proposed that an electron, behaves both as a material particle and as a wave. (c) This proposed a new theory wave mechanical theory of matter. According to this theory, the electrons protons and even atom when in motion possess wave properties (d) According to de-Broglie, the wavelength associated with a particle of mass m, moving with velocity v is given by the relation, h  = mv where h is Planck’s constant. (e) This can be derived as follows according to Planck’s equation h.c  Energy of photon on the basis of Enstein’s mass energy relationship E = mc2 (g) If we associate Bohr’s theory with De-Broglie Equation we find that the wavelength of an electron, moving in Bohr’s orbit is related with its circumference through a whole number multiple 2r = n 2r n From de-Broglie equation or  =  = Thus, h 2r = mv n hc h = mc2 or  =  mc Which is the same of de Broglie relation. (f) 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 1 mv2 = eV 2 m2v2 = 2eVm mv =  = 2eVm = p h 2eVm or mvr = nh 2 16.2 Heisenberg’s uncertainty principle (a) While treating e¯ as a wave it is not possible to ascertain simultaneously the exact position and velocity of the e¯ more precisely at a given instant since the wave is extending throughout a region of space (b) As the photons of longer wavelengths are less energetic, hence they have less momentum and cannot be located exactly (c) In 1927, Werner Heisenberg presented a principle known as Heisenberg’s uncertainty principle (d) According to this principle it is impossible to measure simultaneously the exact position and exact momentum of a body as small as an electron. (e) If uncertainty of measurement of position is x uncertainty of momentum is p or mv. then according to Heisenberg E = h = Equating both h mv x . p  h 4 h 4 where h is planck’s constant (f) For other canonical conjugates of motion the equation for Heisenberg’s uncertainty principle may be given as or x . mv  h (for energy and time) 4 16.3 Schrodinger wave equation (a) Wave mechanical model of an atom was developed on the basis of dual nature of electron by Erwin schrodinger in 1926. (b) In this model electron is described as a three-dimensional wave in the electric field of a positively charged nucleus. (c) This approach is also called probability approach. The probability of finding an electron at any point around the nucleus can be calculated E t  Page # 12 ATOMIC STRUCTURE with the help of schrodinger wave equation. The schrodinger wave equation is 2  2   2 8 2m + + + (E - V) = 0 2 2 y z x 2 h2 where x, y and z are three space coordinates m is the mass of electron h is planck’s constant E is total energy V is potential energy of e¯  is the amplitude of wave also called wave function (d) As we know that the variable quantity in a wave is the amplitude. Similarly we take wave function  in case of de-broglie waves (e) In most of the cases, this wave function is a complex quantity and hence cannot be measured experimentally (f) By performing proper mathematical operations on the wave function () information regarding position, momentum kinetic and potential energy etc. of the particle can be obtained. (g) The most important property of  is that it gives a measure of the probability of finding the electron at a given position around the nucleus. (h) The quantity 2 gives the probability of finding an electron in a unit volume and is called probability density. This definition of probability is in agreement with the uncertainty principle as one cannot talk about the precise position of subatomic particles. 17. QUANTUM NUMBERS (a) The measurement scale by which the orbitals are distinguished, can be represented by sets of numbers called as quantum number. (b) It is a very important number to specify and display to complete information about size, shape and orientation of the orbital. These are principle, azimuthal and magnetic quantum number, which follows directly from solution of schrodinger wave equation. (c) Except of these quantum numbers, one additional quantum number designated as spin quantum number, which specify the spin of electron in an orbital. (d) Each orbital in an atom is specified by a set These quantum numbers are as follows : 17.1 Principal quantum number (n) : (a) It was proposed by Bohr and denoted by ‘n’. (b) It determines the average distance between electron and nucleus, means it is denoted the size of atom. (c) It determine the energy of the electron in an orbit where electron is present. (d) The maximum number of an electron in an orbit represented by this quantum number as 2n2. (e) It gives the information of orbit K, L, M, N, (f) The value of energy increases with the increasing value of n. (g) It represents the major energy shell from which the electron belongs. (h) An orbital momentum of any orbit = nh  17.2 Azimuthal quantum number or angular q u an t u m n u m b er ( l) (a) It was proposed by sommerfeld and denoted by ‘l’. (b) It determines the number of subshells or sublevels to which the electron belongs. (c) It tells about the shape of subshells. (d) It also expresses the energies of subshells s < p < d < f (Increasing energy). (e) The value of l = (n – 1) always where ‘n’ is the number of principle shell. (f) Value of l = 0 1 2 3 ----(n–1) Name of = s p d f subshell Shape of = spherical Dumbbel l Double Complex subshell dumbbell dumbbell (g) It represent the orbital angular momentum, which is equal to h (   1) . 2 (h) The number of electrons in subshell = 2(2l + 1). (i) For a given value of ‘n’ the total value of ‘’ is always equal to the value of ‘n’ . (j) The energy of any electron is depend on the value of n & l because total energy = (n + l). The electron enters in that sub orbit whose (n + l) value or the value of energy is less. 17.3 Magnetic quantum number (m) : (a) It was proposed by Linde and denoted by ‘m’. (b) It gives the number of permitted orientation of subshells. (c) The value of m varies from – l to + l through zero. (d) It tells about the splitting of spectral lines in the magnetic field i.e. this quantum number proved the Zeeman effect. (e) For a given value of ‘n’ the total value of ‘m’ is equal to n2. (f) For a given value of ‘l’ the total value of ‘m’ is equal to (2l + 1). (g) Degenerate orbitals - Orbitals having the same energy are known as degenerate orbitals. e.g. for P subshell P x P y Pz (h) The number of degenerate orbitals of s subshell = 0. Page # 13 ATOMIC STRUCTURE (c) The ‘d’ orbital is bidumb-belled. 17.4 Spin quantum number (s) : (a) It was p roposed by Goldshmidt & Uhlenbeck and denoted by the symbol of ‘S’. (b) The value of ‘s’ is + ½ & – ½, Which is signified the spin or rotation or direction of electron on it’s axis during the movement. (c) The spin may be clockwise & anticlockwise. (d) It represents the value of spin angular h s( s  1) . momentum is equal to  (d) It has directional properties. 19. ELECTRONIC CONFIGURATION PRINCIPLES The distribution of electrons in different orbitals is known as electronic configuration of the atoms. Filling up of orbitals in the ground state of atom is governed by the following rules : 19.1 Aufbau Principle : (e) Maximum spin of an atom = ½ × number of (a) It is a German ward, meaning ‘building up’ unpaired electron. (b) According to this principle, “In the ground state, the atomic orbitals are filled in order of 18. SHAPE OF ORBITALS increasing energies”. i.e. in the ground state Orbital :Orbital is the three dimensional region the electrons occupy the lowest orbitals available around the nucleus where there is a maximum to them. tendency of finding an electron of definite energy (c) The sequence of filling of e¯ we have already 18.1Shape of orbitals on the basis of quantum number 18.1.1Shape of ‘s’ orbital : (a) For ‘s’ orbital  = 0 & m = 0 so ‘s’ orbital have only one unidirectional orientation i.e. the probability of finding the electron is same in all directions. (b) The size and energy of ‘s’ orbital with increasing ‘n’ will be 1s < 2s < 3s < 4s. (c) It does not consist any directional property. 18.1.2Shape of ‘p’ orbitals: (a) For ‘p’ orbital  = 1 & m = +1, 0, – 1 means discussed in previous article (d) In fact the energy of an orbital is determined by the quantum number n and l with the help of (n + l) rule or Bohr Bury rule (e) According to this rule (i) Lower the value of n + l, lower is the energy of the orbital and such an orbital will be filled up first (ii) When two orbitals have same value of (n + ) the orbital having lower value of “n” has lower energy and such an orbital will be filled up first. 19.2 Pauli’s Exclusion Principle : (a) According to this principle, “ No two there are three ‘p’ orbitals, which is symbolised electrons in an atom can have all the four as px, py, pz. quantum numbers n, l, m and s identical. (b) Shape of ‘p’ orbital is dumbbell in which the (b) In an atom, any two electrons may have two lobes on opposite side separated by the three quantum numbers identical but fourth nodal plane. quantum number must be different. (c) p-orbital has directional properties. (c) Since this principle excludes certain possible combinations of quantum numbers for any two 18.1.3Shape of d-orbital: (a) For the ‘d’ orbital  = 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 , dx2 – y2, dz2 . electrons in an atom, it was given the name exclusion principle, Its results are as follows (i) The maximum capacity of a main energy shell is equal to 2n2 electron (b) Each ‘d’ orbital identical in shape, size and (ii) The maximum capacity of a subshell is equal energy. to 2(2l + 1) electrons 1 Page # 14 ATOMIC STRUCTURE (iii) Number of sub-shells in a main energy shell 19.4 (n + l) Rule is equal to the value of n This rule states that electrons are filled in (iv) Number of orbitals in a main energy shell orbitals according to their n + l values. Electrons is equal to n2 are filled in increasing order of their (n + l) (v) one orbital cannot have more than two electrons values. When (n + l) is same for sub energy levels, the electrons first occupy the sublevels (d) According to this principle an orbital can accomod at the most two electrons with their spins opposite to each other. (e) It means that an orbital can have 0, 1, or 2 electron (f) If an orbital has two electrons they must be with lowest “n” value. Thus, order of filling up of orbitals is as follows: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d 20. ENERGY LEVEL DIAGRAM (a) The representation of relative energy levels of opposite spin of various atomic orbital is made in the terms of energy level diagrams. correct Incorrect 19.3 Hund’s Rule of Maximum Multiplicity : (b) One electron system : electron is in 1s2 In thi s system level and all orbital of same (a) This rule governs the filling up of degenerate principal quantum number have same energy, orbitals of the same sub-shell which is independent of (l). In this system l (b) Accordint to this rule “Electron filling will not take place in orbitals of same energy unitill all the available orbital of a given subshell contain one electron each with parallel spin.” (c) This implies that electron pairing begins with fourth, sixth and eighth electron in p, d and f orbitals of the same sub-shell respectively. (d) The reason behind this rule is related to repulsion between identical charged electron only determines the shape of orbital. (c) Multiple electron system : levels of such system not only depend upon the nuclear charge but also upon the another electron present in them 6p 5d 4f 6s 5p 4d (e) They can minimise the repulsive forces 5s 4p orbitals. (f) Moreover, according to this principle, the e¯ E nergy present in the same orbital between them serves by occupying different 3d 4s 3p entering the different orbitals of subshell have parallel spins. This keeps them farther apart 3s and lowers the energy through electron exchange 2p or resonance. (g) The term maximum multiplicity means that the total spin of unpaired e¯ is maximum in case of correct filling of orbitals as per this rule. The energy 2s 1s Page # 15 ATOMIC STRUCTURE Page # 15 ATOMIC STRUCTURE Diagram of multielectron atoms reveals the following points (a) As the distance of the shell increases from the nucleus, the energy level increases. For example energy level of 2 > 1. (b) The different sub shells have different energy levels who have possess definite energy levels. For a definite shell, the subshell having higher value of  possesses higher energy level. For example in 4th shell. Energy level order 4f > l = 3 4d > 4p l = 2 > l = 1 4s l = 0 (c) The relative energy of sub shells of different (b) The energy is released during the exchange process with in the same subshell. (c) In case of half filled and completely filled orbitals, the exchange energy is maximum and is greater then the loss of orbital energy due to the transfer of electron from a higher to a lower sublevel e.g. from 4s to 3d orbitals in case of Cu and Cr (d) The greater the number of possi ble exchanges between the electrons of parallel spins present in the degenerate orbitals, the higher would be the amount of energy released and more will be the stability (e) Let us count the number of exchange that are possible in d4 and d5 configuration among electrons with parallel spins : energy shell can be explained in terms of the (n + ) rule. (i) The subshell with lower values of (n + ) d 4 (1) possess lower energy level. For 3d n = 3  n +  = 5 For 4s 3 exchanges by 1st e¯ l = 2 n = 4 (2) l = 0 2 Exhanges by 2nd e¯ n + l = 4 (ii) If the value of (n + ) for two orbitals is (3) same, one with lower values of ‘n’ possess lower energy level. only 1 exchange by 3rd e¯ Total number of possible exchanges = 3 + 2 + 1 21. EXTRA STABILITY OF HALF FILLED AND COMPLETELY FILLED ORBITALS Half-filled and completely filled sub-shells have extra stability due to the following reasons. 21.1 Symmetry of orbitals : = 6 d5 (1) (a) It is a well known fact that symmetry leads 4 exchanges by 1st e¯ to stability. (b) Thus, if the shift of an electron from one (2) orbital to another orbital differing slightly in 3 exchanges by 2nd e¯ energy results in the symmetrical electronic configuration. it becomes more stable (c) For example p3, d 5, f7 (3) confiogurations are 2 exchanges by 3rd e¯ more stable than their near ones 21.2 Exchange Energy (D) (a) The e¯ in various subshells can exchange their positions, since e¯ in the same subshell have equal energies. 1 1 exchange by 4th e¯ Total number of possible exchanges = 4 + 3 + 2 + 1 = 10 Page # 16 ATOMIC ATOMICSTRUCTURE STRUCTURE 22. ELECTRONIC CONFIGURATION OF ELEMENTS Element H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V *Cr Mn Fe Co Ni *Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr *Nb *Mo Tc *Ru *Rh *Pd *Ag Cd In Sn Sb Te I Xe At.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 1s 2s 2p 3s 3p 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 3d 4s 4p 1 2 3 5 5 6 7 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4d 1 2 4 5 5 7 8 10 10 10 10 10 10 10 10 10 4f 5s 5p 1 2 2 2 1 1 2 1 1 1 2 2 2 2 2 2 2 1 2 3 4 5 6 6d 5f Page # 17 ATOMIC STRUCTURE Element At.No. Cs Ba *La Ce Pr Nd Pm Sm Eu *Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir *Pt *Au Hg Ti Pb Bi Po At Rn Fr Ra *Ac *Th *Pa *U Np Pu Am *Cm *Bk Cf Fs Fm Md No *Lw Ku Ha 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 Page # 17 ATOMIC STRUCTURE K L M 4s 4p 4d 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 4f 5s p 5d 1 3 4 5 6 7 7 9 10 11 12 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5d 5f 6s 6p 0 2 3 4 6 7 7 8 10 11 12 13 14 14 14 14 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 1 1 1 1 2 3 4 5 6 7 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 6d 1 2 1 1 1 1 1 1 2 3 6f 7s 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Page # 18 ATOMIC STRUCTURE 23.RADIO ACTIVITY (a) It is the property of the nucleus of the atom. Radio active element possesses unstable nucleus. (b) It is discovered by Henery Becqural. (c) The unstable nucleus gives   e – 1e º j 2 He 4 or particles and the product is nucleus of another element. During – or  – emission the energy is emitted in the form of  – radiation. 23.1 Nuclear forces : (a) The force of attraction which binds protons & neutrons (nucleons) mutually is called as nuclear force. (b) According to modern approach, nuclear force arises by the exchange of mesons between nuclear particles. (c) Nuclear forces are stronger than repulsion forces between protons (having same charge). (d) Due to exchange of mesons, exchange forces arise which binds nuclear particles to one another. n+    p p +    n or (e) Between two protons & two neutrons, neutral meson particles (º) are exchanged. nucleus formation 127 Mev energy releases – which is called its binding energy. 23.3 Relation between mass defect & binding energy : (a) Equivalent energy corresponding to mass defect is known as binding energy. (b) If m mass defect occurs in the formation of a nucleus from nucleus particles then binding energy will be written as BEn =  m × 931 Mev. (c) Einstein equation is written as E = mc2 where E = Energy (arg.) M = mol. wt. (gram) C = velocity of light (cm/sec.) According to the equation– Equivalent energy of 1 amu mass is 931 Mev. So BEn = m × 931 Mev. 23.4 Binding energy per nucleon : (a) Binding energy per nucleon is the measure of stability of the nucleus. (b) Relative stability of isotopes and binding energy : Consider the hypothetical nuclear reaction : zX A neutron    zX A1[  PMe V ] zX A neutron    zX A 2 [  Q Me V ] (c) If the value of binding energy is positive then, The stability order is Product nucleus > reactant nucleus 23.2 Mass defect & binding energy of nucleus : (a) The original mass of an atom is less than the total mass of original particles. (b) When a stable nucleus is formed by protons & neutrons then a part of mass converts in energy & disappears so the mass of atomic nucleus is reduced as compared to total mass of nuclear particles by which it is formed. (c) This loss of mass is called as mass defect. Mass defect = (Total mass of nuclear particles)– (original mass of nucleus) (d) When nuclear particles (protons & neutrons) form a stable atomic nucleus then mass defect takes place and energy emits which is called binding energy of nucleus.For e.g. in oxygen If the value of binding energy is negative then the stability order is Product nucleus < reactant nucleus 23.5 Nuclear stability & the ratio of neutrons & protons : (a) The stability of nucleus depends upon the ratio of neutrons (n) & protons (p) (b) The nucleus in which n 1 (approx), are p very stable. (c) When this ratio exceeds 1.5, then nucleus becomes unstable and radioactive. (d) This ratio is approx. 1 (one) up to atomic number 1 to 20 & the atomic number above 83 the ratio is 1.5 to 1.6. So these atoms are radioactive. Page # 19 ATOMIC STRUCTURE for eg. in in 235 92 U , n 20   1 so nucleus is stable. p 20 (iii)They have same chemical properties because n 235   155 . , so nucleus is unstable. p 92 (iv)They have different physical properties 40Ca, 24. SOME IMPORTANT DEFINITIONS they have same atomic number. because they have different atomic masses. eg. 1H 1 1H Protonium deuterium 2 1H 3 Tritium Z = 1 1 1 A = 1 2 3 (g) Isobar : The two different atoms which have same atomic (a) Nodal Surface : The place find in between two ‘s’ orbitals where the value of electron density is equal to zero called Nodal surface. masses but different atomic number is called as Isobar. eg. 18 Ar 19 K Atomic 40 The number of Nodal surfaces in an atom = mass (n – 1), where ‘n’ is the number of total shell in an atom. Atomic 18 (b) Nodal Plane : 40 (h) Isomorphous : For Isomorphous py = xz Isomorphism. pz = xy eg. th is property call ed ZnSO4 . 7H2O Hepta hydrate Hepta hydrate Ferrous Zinc Sulphate dz2 = (i) Isomers : (d) Isodiapheres : The elements which have same value of (n – p) is called Isodiapheres. 14 16 eg. 7N 8O Values of (n – p) 0 0 (e) Isotone : Elements which contain same no. of neutron is called Isotone. 30 31 32 eg. 14 Si 15P 16 S number of neutrons 16 16 (f) Isotopes : (i) First proposed by soddy. (ii) The isotopes have same atomic number but different atomic weight. an d White vitriol sulphate The nucleus of an atom called Nodal Point. 20 Green vitriol = xy, yz (c) Nodal Point : 19 FeSO4 . 7H2O dzx 0 40 contain same crystall ine structure called = yz dyz = xy, xz dx2–y2 = 0 40 40 The two different type of compound which px dxy = yz, zx 20 Ca number The place for ‘p’ and ‘d’ orbitals where the value of electron density is equal to zero called Nodal Plane. For 40 Species which have same molecular formula but different structural formula is called Isomer and this type of property is called Isomerism. eg. C2H6O  C2H5 OH & CH3 – O – CH3 (j) Isoelectronic : Ion or atom or molecule or species which have the same nu mber of el ectron is cal l ed Isoelectronic species. eg. 17 Cl No. of 18 – 18 Ar 19K 18 18 + 20 Ca +2 18 electron eg. CN– CO No. of electron 14 14 Page # 20 ATOMIC STRUCTURE (k) Isosters : Note : When an electron is in the stationary Substance which have same number of electron and atoms called Isosters. state then the value of magnetic field for that eg. CO2 N2O 22 22 electron is equal to zero. (q) Promotion : (l) Kernel : Orbit which present after removing the outer most orbit of that atom is called kernel and electrons which is present that orbit called kernel electrons. The transfer of electron between subshells in eg. Mg = 1s2 2s2 2p6 , 3s2 transition. After the completion of promotion Total kernel electron = 2 + 2 + 6 = 10 the transition process is occurred. (m)Core : (i) The outer most shell of an any atom called Core and the number of electron present of that shell is called Core electron. eg. Cl = 1s2 2s2 2p6 3s2 3p5 an orbit is called promotion. While the transfer of one energy level to another is called eg. First promotion of an electron is 2s (n + = 2 + 0 = 2) to 2p (n +   = 2 + 1 = 3) sub- shell and their transition to 2nd orbit to 3rd orbit or 2p to 3s. Core electron= 2 + 5 = 7 (ii) If the core is unstable for an atom then that atom shows variable valency. 25. SOME IMPORTANT POINTS  (n) Photoelectric effect : When a beam of light of high frequency is strike on a metal surface in vacuum condition, electrons are emitted from the metal surface. This phenomenon is called photoelectric effect and the emi tted electron is cal led photoelectrons.  Total energy = ½mv2 + The wave character is of no significance in case of large objects like cricket ball, a car, a train etc.  The most important applications of de-Broglie concept is in the construction of electron microscope and the study of surface structure of solids by electron diffraction. {½ mv2 = kinetic energy  Smaller the wavelength of the electron  = Threshold energy or work function} wave, more is the resolving power of the electron microscope (o) Threshold energy : The minimum energy required to emit an electron on the metal surface called threshold energy. (p) The value of equal to - e for n, p, , & electron is m e for n = 0 m e 2  16 .  1019 for  = = 4.8 × 105 m 4  167 .  1024 16 .  10 19 e for p = 167 .  1024 m e for e– = m = 1.6  10 19 9.1  10 28 1 9.58 × 104 = 1.76 × 108  Uncertainty in measurement is not due to lack of any experimental technique but due to nature of subatomic particle itself  Shapes of orbi tals are functional representation of mathematical solutions of Schrodinger equations. They do not represent any picture of electric charge or matter.