GENERAL CHEMISTRY: CHAPTER NINE1.1 Electromagnetic Radiation.1.2.2 The Photoelectric Effect. Thus the electron takes adopts the left over energy:1.2.3 The Hydrogen Line Spectrum.2.1 The Bohr Atom.2.2 Atomic Spectroscopy.3.1 The Uncertainty Principle. 3.2 The Duality Hypothesis. 3.3 Schrodingers Equation.3.5 The Schrodinger Hydrogen Atom.GENERAL CHEMISTRY: CHAPTER NINE QUANTUM CHEMISTRY 1 INTRODUCTION. Most of the major theories of atomic and molecular structure that are used in modern chemistry owe their origin to the application of quantum mechanics. What is now called old quantum theory first appeared in 1900 in a publication by the German physicist Max Planck. We shall not go into the intimate details of the historical development of quantum theory, nor shall we be concerned with its complicated mathematical methodology. It is , however, appropriate for us to identify some of the high points in the evolution of quantum mechanics and to get some kind of comprehension of the spirit of its implications. We need first to cast our minds back to the last ten years of the nineteenth century. The science of physics had witnessed some incredible advances in the preceding decades. Numerous phenomena that had previously defied any sort of rational 1explanation were no longer mysteries. There were, however, a number of observations that had been verified in many laboratories but had eluded any satisfactory explanation. Three of those “mysterious” observations stand out as playing a special role in the history of modern physics. They are: 1) The Black-Body Radiation Spectrum. 2) The Photoelectric Effect. 3) The Hydrogen Line Spectrum. All three of these phenomena involve interactions between matter and radiation. The most immediate impact of Planck’s quantum theory was to change the world’s perception of the nature of radiation. 1.1 Electromagnetic Radiation. Sir Isaac Newton was a quarrelsome person. In his lifetime, he was involved in two major arguments. The first argument was with the German mathematician Liebnitz, on the question of who should take credit for the development of calculus. The second was with the Dutch scientist Huyghens about the nature of light. Isaac Newton 2The difference of opinion about light was quite clear. Newton proposed that light must have a corpuscular character. In other words there must be discrete light particles. Huyghens idea was that light is essentially a continuous wave phenomenon. Since the phenomenon of refraction, in which light is bent passing from one medium to another, could not be explained in terms of a particle theory, Newton conceded that the wave theory was that more plausible He prophesied that the issue was not altogether resolved. Christiaan Huyghens The wave theory received compelling support from the results of the dual slit interference experiments of Thomas Young in 1800. The diffraction phenomenon could be readily explained by the wave theory but was judged to be totally foreign to any kind of corpuscular existence. 3During the 19th century a substantial amount of progress was made in the development of theories of electromagnetic radiation, of which visible light is only one type. The figure illustrates the generation of oscillating electric and magnetic fields that are mutually perpendicular and perpendicular to the direction of the radiation’s propagation. The wave moves with a speed c ( = 3.00 x 108 m s-1). It is the same speed for all types of radiation. The distance between successive peaks of the wave is called the wave- length of the radiation. Wavelengths vary from 10-13 m up to 104 m. The following diagram matches wavelengths to different types of radiation. 4The visible spectrum is very narrow, when compared to the total range for all types of electromagnetic radiation. Each color of the visible spectrum has a distinct range of wavelengths. White light is made up of “all of the colors of the rainbow”. Light of a single wavelength is said to be monochromatic. Many waves pass a given point every second. The number of waves per second is called the frequency of the radiation. The unit of one cycle per second is most frequently referred to by its SI name: Hertz, Hz. The product of the frequency, ν (s-1), and the wavelength, λ (m), is the speed of light, c (m s-1). c = ν λ 5The table shows a few typical frequency values for the different types of radiation. One notes that the values given need to be multiplied by 1014 Hz. It may be helpful to calculate the wavelength of the waves coming from your favorite radio station. AM stations typically transmit in the 500 – 2000 kHz range. They correspond to wavelengths ranging from 150 – 600 m. FM stations have much higher frequencies (80 – 120 MHz). They correspond to much shorter wavelengths (2.5 – 4 m). 1.2 THREE CRITICAL EXPERIMENTS. 1.2.1 The Black-Body radiation Spectrum. When white light encounters an object that appears to us to be colored, that object has absorbed part of the visible spectrum. The remainder is reflected. It is the reflected light that gives the object the appearance of being colored. 6Objects that do not absorb any visible radiation reflect the entire rainbow and appear to us to be white. Objects that absorb all visible frequencies are called black bodies. When an object is heated, it emits the same wavelengths of radiation that it absorbs when it is cold. A black body emits all of the colors of the visible spectrum in addition to the lower frequency infra – red and the higher frequency ultra-violet radiation. During the latter half of the nineteenth century, physicists in many laboratories measured the intensities of light of different frequencies to produce black – body radiation spectra. The following figure shows two such spectra recorded at different temperatures. Theories of the emission of radiation predicted the shape of the curve at low frequencies (large wavelengths) correctly but offered no explanation for the existence of the maximum. Statistical treatments of heat loss could predict the high frequency end of the curve, but again failed to account for the maximum. Max Planck sought an explanation for the shape of the experimental curve and for the effect of temperature upon the frequency of the most intense radiation. He 7concluded that the curves could only be explained in terms of