Principles of Chemistry I
Principles of Chemistry I CHEM 1211
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CHEM 1211 Principles of Chemistry I Chapter 7 Atomic Structure and Periodicity 71 Electromagnetic Radiation one of the ways that energy travels thought space is by electromagnetic radiation examples are cosmic rays gamma rays xrays ultraviolet rays visible rays in a red rays microwaves radio waves 0 these forms of radiation seem different but they all exhibit the same type of wavelike behavior and travel at the speed of light in a vacuum waves have three characteristics 0 1 wavelength 0 2 frequency and O 3 speed wavelength symbol 9 is the distance between two consecutive peaks or troughs in a wave 0 see Figure 71 frequency symbol v is de ned as the number of waves cycles per second that pass a given point in space have the relation 9 in meters gtlt v cycles per second Hz 108 ms 0 see Figure 72 c the speed of light 2998 X 72 The Nature of Matter 0 the rst important advance in understanding the nature of matter came in 1900 from the German physicist Max Planck 1858 1946 O studying the radiation pro les emitted by solid bodies heated to incandescence Planck found that the results could not be explained in terms of the physics of his day which held that matter could absorb or emit any quantity of energy 0 Planck could only account for these observations by postulating that energy can be gained or lost only in wholenumber multiples of the quantity hv where h is known as Planck s constant determined by experiment to have a value of 6626 X 10 J s 0 thus the change in energy for a system A E can be represented by the equation A E nhv where n is an integer 1 2 3 h is Planck s constant and n is the equency of the EMR absorbed or emitted O Planck s result was a real surprise it had always been assumed that the energy of matter was continuous which meant that the transfer of any quantity of energy was possible 0 now it seemed clear that energy is in fact quantized and can only occur in discrete units of size 0 these packets of energy are called quanta singular quantum 0 next development occurred when the German physicist Albert Einstein proposed that electromagnetic radiation is itself quantized RFGCSU Page 1 of 6 Ch 07 Zumdahl 7th edwpd O Einstein suggested that electromagnetic radiation can be viewed as a stream of particles called photons O the energy of each photon given by Ephmn hv hd O in a related development Einstein derived the famous equation E mc2 see Figure 74 73 The Atomic Spectrum of Hydrogen another important experiment that produced information about the atom was the study of the emission of light by excited hydrogen atoms 0 when a sample of hydrogen gas receives a highenergy spark the H2 molecules absorb energy and some of the HH bonds are broken 0 the resulting hydrogen atoms are excited ie they contain excess energy which they release by emitting light of various wavelengths to produce what is called the emission spectrum of the hydrogen atom continuous versus line spectrum what is the signi cance of the line spectrum of hydrogen it indicates that only certain energies are allowed for the electron in the hydrogen in the hydrogen atom 0 see Figure 77 74 The Bohr Model 0 in 1913 a Danish physicist named Niels Bohr 18851962 aware of the experimental results discussed developed a quantum model for the hydrogen atom O Bohr proposed that the electron in a hydrogen atom moves around the nucleus only in certain allowed orbits 0 he calculated the radii for these allowed orbits by using the theories of classical physics and by making some new assumptions see Figure 78 O the most important equation to come from Bohr s model is the expression for the energy levels available to the electron in the hydrogen atom see Equation 71 note 11 is an integer the larger the value of n the larger is the orbit radius and Z is the nuclear charge 0 using this equation Bohr was able to calculate hydrogen atom energy levels that exactly matched the values obtained by experiment 0 two points about the Bohr model need to be emphasized 1 The model correctly fits the quantized energy levels of the hydrogen atom and postulates only certain allowed circular orbits for the electron 2 As the electron becomes more tightly bound its energy becomes more negative relative to the zeroenergy reference state corresponding to the electron being at infinite distance from the nucleus As the electron is brought closer to the nucleus energy is released from the system 0 Bohr s model only works for hydrogen the model is fundamentally incorrect 0 current theory of atomic structure is in now way derived from the Bohr model RFGCSU Page 2 of 6 Ch 07 Zumdahl 7th edwpd O electrons do not move around the nucleus in circular orbits 75 The Quantum Mechanical Model of the Atom 0 after the failure of the Bohr model for multielectron atoms a totally new approach was needed 0 Werner Heisenberg 19011976 Louis de Broglie 18921987 and Erwin Schrodinger 18871961 were the physicists that led the new effort 0 the approach they developed became known as wave mechanics or more commonly quantum mechanics 0 the key was to attack the problem of atomic structure by giving emphasis to the wave properties of the electron see Figure 710 O in 1925 Schrodinger developed an equation that bears his name 0 Heisenberg s mathematical analysis led him to a surprising conclusion there is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time known as the Heisenberg uncertainty principle 0 applied to the electron the uncertainty principle implies that we cannot know the exact motion of the electron as it moves around the nucleus not appropriate to assume that the electron is moving around the nucleus in a welldefined orbit as in the Bohr model speak of probabilities 76 Quantum Numbers 0 when the Schrodinger equation is solved for the hydrogen atom many wave mctions orbitals are found that satisfy it 0 each of these orbitals is characterized by a series of numbers called quantum numbers which describe various properties of the orbital O the principal quantum number n has integral values 1 2 3 the principal quantum number is related to the size and energy of the orbital O the angular momentum quantum number 0 has integral values from 0 to 111 for each value of n O the magnetic quantum number m I has integral values between I and l including 0 see Table 71 and 72 77 Orbital Shapes and Energies see Figure 713 see Figure 714 see Figure 716 see Figure 717 see Figure 718 RFGCSU Page3 of 6 Ch 07 Zumdahl 7th edwpd 78 Electron Spin and the Pauli Principle the concept of electron spin was developed by Samuel Goudsmit and George Uhlenbeck while they were graduate students at the University of Leyden in the Netherlands 0 they found that a fotuth quantum number was necessary to account for the details of the emission spectra of atoms 0 the data indicate that the electron has a magnetic moment with two possible orientations when the atom is placed in an external magnetic eld 0 the electron spin quantum number ms can have only one of two values 12 and see Figure 719 the main signi cance of electron spin is connected with postulate of Austrian physicist Wolfgang Pauli 19001958 in a given atom no two electrons can have the same set of four quantum numbers Pauli Exclusion Principle 79 Polyelectronic Atoms read on your own 710 The History of the Periodic Table RFGCSU the periodic law did not occur to anyone until 1869 although considerable information was available concerning the thenknown elements in 1817 Johann Wolfgang Dobereiner 17801849 saw trends and similarities along several groups of three elements which he called triads by 1862 AlexandreEmile Beguyer de Chancourtois 18201886 saw similarities in elements along vertical lines when the elements were arranged in order of their atomic weights along a helix in 1864 when John Newlands 1837 1898 arranged element in the order of their atomic weights and observed that every eighth element had similar properties coined the term quotlaw of octavesquot 0 these early ideas were incomplete and gained no lasting support a Russian Dmitri Ivanovitch Mendeleev 18341907 in 1869 organized the elements by atomic weight recognized there was a trend in properties that repeated itself several times the periodic law and table were born although only 63 elements had been discovered by 1869 noble gases weren39t discover until after 1893 and the clarifying concept of the atomic number was not known until 1913 O Mendeleev published a more elaborate periodic table in 1871 this version is the forerunner of the modern table 0 see Figure 724 0 two features 1 empty spaces were left in the table and 2 problem with the positions of Te and I spaces were lled by the discoveries of Ga 1875 and Ge 1886 Page4of 6 Ch 07 Zumdahl 7th edwpd u see Table 73 0 1 r w number concept In 1913 the question was iesolved t M d l sir A It dld I o the modem penodlc law states 0 to h 1 a physlc l propemes show ispealableliends 711 The Aufbau Princip1e and the Periodic Table 1 t M t hydmgenrhke orbitals lhls is called the Allfball pnnclple 0 see illustrations in text fox hydrogen through bomn prinu39plein a par cidar set nfrlegenerate orbitals 0 0h t r ofan atom o in bonding u inner electrons are known as core electrons elections u see Figure 723 712 Periodic Trends in Atomic Pmpem es u mllconsldex 110nlz hon eneigy o 2electrohat1imtyahd o 3atcrmcsize o Ionimcn Energy X XYQ rE39 macsu page 5 of o Ch o7 Zumdzhl 7111 ed wpd
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