Lecture 3 Atomic-Structure PDF

1 General Chemistry I Atomic Structure  Content The Structure of the Atom Atomic Spectra Electron Orbitals and Quantum Numbers Quantum Energy Levels in Atoms Basic Concepts of Bonding Electronegativities Lewis Structure The Octet Rule Dipole Moment Resonance Orbital...

1 General Chemistry I Atomic Structure  Content The Structure of the Atom Atomic Spectra Electron Orbitals and Quantum Numbers Quantum Energy Levels in Atoms Basic Concepts of Bonding Electronegativities Lewis Structure The Octet Rule Dipole Moment Resonance Orbital Configuration for Diatomic Molecules Geometrics of Molecules Hybridization in Molecules 3  Aristotle (384–322 BC) Believed all matter came from only four elements: earth, air, fire and water The ideas of these early philosophers prevailed for 2000 years… 4  Empedocles (490–430 BC) (2500 years ago) Everything in existence is made of different combinations of four pure and indestructible elements: air, fire, water and earth 5  1- Atomic Structure (Historic introduction) ◼ Matter could not be divided into smaller and 400 BC smaller pieces forever, eventually the smallest possible piece would be obtained. ◼ This piece would be indivisible. ◼ Democritus named the smallest piece of matter Democritus “atomos,” the Greek word for “indivisible.” To Democritus: ❑ Atoms were infinite in number, always moving and capable of joining together. ❑ Atoms were small, hard particles that were all made of the same material but were different shapes and sizes. 6  Historic introduction John Dalton (England 1766-1844) ◼ Studied the ratios in which elements combine in chemical reactions ◼ 1803: Formulated first modern Atomic Theory ◼ Billiard Ball Model 7  Historic introduction Dalton’s atomic theory of matter 1. All elements are composed (made up) of atoms. It is impossible to divide or destroy an atom. 2. All atoms of the same element are alike. (One atom of oxygen is like another atom of oxygen.) 3. Atoms of different elements are different. (An atom of oxygen is different than an atom of hydrogen) 4. Atoms of different elements combine to form a compound. These atoms have to be in definite whole number ratios. For example, water is a compound made up of 2 atoms of hydrogen and one atom of oxygen. (A ratio of 2:1) Three atoms of hydrogen and 2 atoms of oxygen cannot combine to make water. 5. Chemical reactions occur when atoms are separated, joined, or rearranged. Atoms of one element are never changed into atoms of another element as a result of a chemical reaction. 8  Historic introduction Thomson’s (1856-1940) ◼ In 1897, the English scientist J.J. Thomson provided the first hint that an atom is made of even smaller particles. ◼ Received 1906 Nobel Prize in Physics. J. J. Thomson – using the cathode ray tube he observed a flow of negatively charged particles he identified as electrons. ◼ Thomson measured mass-to-charge of e - e/m for the electron = -1.76 x 108 C/g ◼ Millikan determined the charge of e- 9 10  Historic introduction The Cathode Ray Tube ◼ For years scientists had known that if an electric current was passed through a tube containing a gas, a stream of glowing material could be seen; however, no one could explain why. ◼ Thomson found that the mysterious glowing stream would bend toward a positively charged electric plate. ◼ Thomson theorized, and was later proven correct, that the stream was in fact made up of small particles, pieces of atoms that carried a negative charge. ◼ These particles were later named electrons. 11 Cathode Ray Tube (CRT) Monitors 12 13  Historic introduction Plum Pudding Model (1904) Thompson developed the idea that an atom was made up of electrons scattered unevenly within an elastic sphere surrounded by a soup of positive charge to balance the electron's charge. 14 15  Historic introduction Ernest Rutherford (1871-1937) Tested Thomson’s theory of atomic structure with the “gold foil” experiment in1910. ⚫ Rutherford’s experiment Involved firing a stream of tiny positively charged (He2+) particles at a thin sheet of gold foil (2000 atoms thick) 16 Rutherford’s Experiment: Prediction according to Thomson’s model mass and positive charge so... of gold atom are too particles should shoot straight dispersed to deflect the through the gold atoms. positively-charged alpha particles 17  Historic introduction (b) Actual results. ❑ Most alpha particles went straight through, ❑ Some were deflected, ❑ Few (1 in 20,000) reflected straight back to the source! 18  Historic introduction gold atom has small, dense, positively-charged nucleus surrounded by “mostly empty” space in which the electrons must + exist. tiny solar system + 19  Historic introduction Rutherford atomic model is known as the nuclear atom In the nuclear atom, protons are located ¯ ¯ in the nucleus. +n ¯ The electrons are distributed around ¯ the nucleus and occupy almost all ¯ ¯ ¯ the volume of the atom. The nucleus is tiny compared with the atom as a whole. Although an improvement over Thomson’s model of the atom, Rutherford’s model turned out to be incomplete and had to be modified 20 Waves 21  The Wave Nature of Light Maxwell (1873), proposed that visible light consists of electromagnetic waves. All waves have a characteristic wavelength, , and amplitude, A. Frequency, , of a wave is the number of cycles which pass a point in one second. Speed of a wave, c, is given by: c =   Speed of light (c) in vacuum = 3.00 x 108 m/s 22  - wavelength - distance between consecutive peaks - crests - measured in m, nm, angstroms. -frequency - number of times per second a crest passes a given point (cycles per second) measured in. c where c = speed of light = 2.998 x 108 m.s-1 =  = m.s-1/m = s-1 = 1 where = wavenumber (m-1 or cm-1)  ◼ Planck’s hypothesis: An object can hc only gain or lose energy by absorbing E = h = = h c or emitting radiant energy in  QUANTA (h). 23 1. The wavelength () is the distance between two similar points on two successive waves (The distance from crest to crest or trough to trough). 2. The amplitude (a) is the height of a crest or the depth of a trough. The intensity or brightness of the radiation α a2. 3. In a vacuum, all waves travel at the same speed, c = 3 x 108 m/s. This speed is called the speed of light. 4. The frequency (), is the number of waves that pass a given spot in a second. c =   Electromagnetic Spectrum 1Ao = 10-10 m = 10-8 cm 1 nm = 10-9 m = 10-7 cm  continuous spectrum White light can be separated into a continuous spectrum of colors. Note that there are no dark spots on the continuous spectrum that would correspond to different lines.  Light passing through an atomic gas shows an absorption line spectrum Emission spectrum is observed when the absorbed light is re-emitted 27 Atomic spectra in the visible region for some elements (a) Emission spectra for some elements (b) Absorption spectrum for hydrogen 28 In 1900, Max Planck proposed the quantum theory of radiant energy. He suggested that radiant energy could be absorbed or given off only in a definite quantities, called quanta. “Planck constant” h = 6.626 x 10-34 J.S In 1905, Albert Einstein proposed that Planck’s quanta are discontinuous bits of energy called photons. c h E= mc2 h = mc2 But = =  mc Balmer-Rydberg equation ◼ The wavelengths of the various lines in the hydrogen spectrum can be related by a mathematical equation ◼ R = 109737 cm-1 (Rydberg constant) ◼ It is thus an empirical equation ◼ Both n1 and n2 are positive integers, and n1 is smaller than n2 30 Bohr Theory (1913) 1- The hydrogen atom contains one electron and a nucleus that consist of a single proton. 2- The electron can exists only in certain spherical orbits called energy levels or shells. 3- The electron has a definite energy characteristic of the orbit in which its moving. 4- When the atoms are heated in an electric arc or Bunsen flame, electrons absorb energy and jumps to outer levels. When an electron falls back to a lower level, it emits a definite amount of energy. The light emitted has a characteristic  and produces a characteristic spectral line. Each line corresponds to a different electron transition.  http://www-groups.dcs.st-and.ac.uk/~history/BigP Bohr Model of the Atom (1913) ◼ In 1913 Bohr provided an explanation of atomic spectra that includes some features of the currently accepted theory Bohr’s Assumptions Neils Bohr (1913) 1) The electron moves in circular orbits around the nucleus under the electric force of attraction  The force produces the centripetal acceleration  Similar to the structural model of the Solar System 32 2) Only certain electron orbits Electron are stable and these are the orbit only orbits in which the + electron is found  These are the orbits in which the atom does not emit energy in the form of electromagnetic radiation  The energy of the atom remains constant  This claims the centripetally accelerated electron does not emit energy and eventually spirals into the nucleus 33  Bohr orbits According to Bohr model only certain orbits are allowed and these orbits are quantized. quantum numbers Orbit numbers describes the (quantum numbers) 4 position of the orbit Electrons in 3 from the nucleus. permitted orbits 2 1 r ◼ Planck’s hypothesis: An object can only gain or lose energy by absorbing or emitting radiant energy in QUANTA (h). Electrons are not allowed 34 between orbits  v me Value of r based on quantum number (n) r n = quantum number r = k x n2 k = constant +  0h 2 h = Planck’s constant k= = 52.918 pm = 6.626 x 10-34 Js mee 2 me = 9.109 x 10-31kg (electron mass when stationary) e = electron charge = -1.602 x 10-19 C,  0h 2 ε0 = permittivity of vacuum r=n 2 mee 2 = 8.854 x 10-14 J-1C2m-1, and  =3.142. 35   0h 2 For Hydrogen atom, n=1 r = a0 = mee 2 ◼A general expression for the radius of any orbit in hydrogen atom is rn = n a0 2 a0 a0 is called the Bohr radius. It’s the radius of the Hydrogen atom (in its lowest-energy, or “ground,” state). 36 The Energies in Hydrogen Atom and hydrogen-like species (one-electron species) v me His hydrogen atom consists of a small nucleus of mass mn around which one small negatively charged r electron of mass me moving in orbit + with radius r and orbital velocity v. The total energy, E, of the electron is the sum of the kinetic energy, KE, and the potential energy, PE. E = KE + PE 37  For an electron of mass m, moving with a velocity v in an orbit of radius r, v me ◼ Coulomb attractive forces. Between the electron and the positively charged nucleus. It attracts the electron to the nucleus and keeps it r revolving in its orbit. + ◼ Centrifugal forces. It repels the electron away from the nucleus. Both forces act in opposite directions. Bohr assumed both forces must be equal to keep electron revolving in its orbit. 38  2 me v Centrifugal force = r If the charge on the electron is e, the number of charges on the nucleus Z and the permittivity of vacuum is o, then 2 Ze Columbic attractive force = 4 o r 2 Both forces act in opposite directions. Bohr assumed both forces must be equal to keep electron revolving in its orbit. 2 2 2 Ze me v = Ze v = 2 r 4 o r 2 4 o mr 39  E = PE + KE − Ze 2 2 2 me v Ze = 4 0 r 2 8 0 r  0h 2 Ze 2 Substituting r=n 2 and v = 2 mee 2 4 o mr − Zmee 4 Zmee 4 Zmee 4 k' Total energy = 2 2 2 + 2 2 2 = − 2 2 2 = − 2 4 0 n h 8 0 n h 8 0 n h n 40 3)The electronic energy is quantized; that is, only certain values of electronic energy are possible. Quantized? continuous quantized An electron can only have certain “allowed energies” no in-between values can exist. 41  4)Electrons can only be in certain discrete orbits, and that they absorb or emit energy in discrete amounts as they move from one orbit to another. hc E = h = = h c  ◼ Atomic states  Excited state – atom with excess energy  Ground state – atom in the lowest possible state ◼ When an H atom absorbs energy from an outside source it enters an excited state. When excitation terminates, the atom can release the extra energy in form emission. Absorption and Emission42 5) Each line in a spectrum is produced when an electron moves from one orbit (stationary state) to another. 43 Classification of spectral lines in hydrogen spectrum Discovered Spectral series Appearing in by i Lyman series Lyman Ultraviolet region ii Balmer series Balmer Visible region iii Paschen series Paschen Infra-red region Far Infra-red iv Brackett series Brackett region Far Infra-red v Pfund series Pfund region 44 Table 2 series of lines in the hydrogen spectrum Series n1 n2 Lyman 1 2, 3, 4, …….……………  Balmer 2 3, 4, 5, …….……………  Paschen 3 4, 5, 6, …….……………  Brackett 4 5, 6, 7, …….……………  Pfund 5 6, 7, 8, …….……………  45  1 11  111 111   v =vv  = = Rn 22−−− = R         2 2 2   n11 n 1nnn  2 2 2  2 ◼ where n1 and n2 are integers and R is the Rydberg’s constant for hydrogen (~ 109678 cm–1). 109737 46 1. Lyman series: This series arises when an electron jumps from any outer orbit to the first orbit, and it lies in the ultraviolet region of the spectrum. Here n1 = 1 and n2 = 2, 3, 4, 5, ………….. The relation can be written as: 1 1 1  ν = = R 2 - 2  λ 1 n2  ν is the wavenumber This series was predicted by Bohr and was photographed by Lyman. 47 2. Balmer series: It originates when an electron jumps from an outer orbit to the second orbit, i.e. n1 = 2 and n2 = 3, 4, 5, … Thus the relation modifies to: 1  1 1  ν = = R 2 - 2  λ 2 n2  n2 = 3 first line of Balmer series n2 = 4 second line of Balmer series n2 = 5 third line of Balmer series 48 3. Paschen series: This originates when an electron jumps from an outer orbit to the 3rd orbit, and falls in the infra-red region of the spectrum, i.e. n1 = 3 and n2 = 4, 5, 6, … The relation takes the form: 111 111 111 vvv=== ===RRR 222−−− 222  333 nnn222 49 4. Brackett series: This also falls in the infra–red region and originates when an electron jumps from an outer orbit to the 4th orbit, i.e. n1 = 4 and n2 = 5, 6, 7, … The relation becomes: 11 1 111 111  = = vv = == RR    − − −    2   2 22 44 4 nn 2 2 2n 2  2 50 5. Pfund series: This again lies in the infra-red region and results when an electron jumps from an outer orbit to the 5th orbit, i.e. n1=5 and n2 = 6, 7, 8 the relation takes the form: 1  1 1  ν = =R  2 - 2 λ 5 n2  51 nfinal = 1 UV [122, 103, 97, …] nm Lyman 1 1 1 nfinal = 2 Visible [656, 486, 434, …] nm Balmer = R( 2 − 2 ) nfinal = 3 IR [1875, 1282, 1094, …] nm Paschen  n final nintial nfinal = 4 IR [4051, 2625, 2165, …] nm Brackett Where RH = 1.096776 x 107 m-1 nfinal = 5 IR [7458, 4652, …] nm Pfundt 52  Hydrogen spectrum according to Bohr Theory For a transition between an initial level (n’) and final level (n), the energy associated with the transition can be found as follows: ' k En' = − 2 (n' ) ' k En = − 2 n ' ' E = − k k 1 − (− 2 ) = k ' ( 2 − 1 k' 2 2 ) R= ( n' ) n n ( n' ) hc 11  11 11  E = h c v =v R = R  −−   2    41 n 2 2 n 2 2  n 53  The experimental value of R obtained by Rydberg was R = 109737 cm-1 The calculated value using Bohr’s derived equation for the hydrogen atom is 109677 cm-1 This validates Bohr’s theory of the atom and it explains all the observed atomic spectral lines of the hydrogen atom just like Rydberg’s equation did. 54  Bohr’s formula for atomic radius rn = n a0 2 n = 1, 2, 3, … and a0 is constant Note: atomic radius is directly proportional to n Bohr’s expression for the energy of the hydrogen atom k' En = − 2 n Note: energy is directly proportional to n 55 Success and failure of Bohr model ◼ Explained several features of the hydrogen spectrum  Accounts for Balmer and other series (explains the spectra of the hydrogen atom)  Predicts a value for R (Rydberg constant) that agrees with the experimental value  Gives an expression for the radius of the atom  Predicts energy levels of hydrogen  Gives a model of what the atom looks like and how it behaves ◼ Can be extended to “hydrogen-like” atoms  Those with one electron (He+, Li2+, Be3+, …) 56 ◼ Bohr model for hydrogen atom and the idea of an electron circling the nucleus is simple and the concept gained widespread acceptance. ◼ However it soon became clear that it did not tell the whole story!!!! PROBLEMS WITH THE BOHR ATOM 1) It is only successful with the hydrogen atom (fails for atoms with more than one electron) 2) It could not account for extra lines in the H emission spectrum when a magnetic field was applied to the gas. 57