Chapter 30: Atomic Physics PDF

Chapter 30:Atomic Physics Mrs. Pooja Brahmaiahchari Introduction Invisible to the eye, the existence and properties of atoms are used to explain many phenomena. In this chapter, we discuss the discovery of atoms and their own substructures; We then apply quantum mechanic...

Chapter 30:Atomic Physics Mrs. Pooja Brahmaiahchari Introduction Invisible to the eye, the existence and properties of atoms are used to explain many phenomena. In this chapter, we discuss the discovery of atoms and their own substructures; We then apply quantum mechanics to the description of atoms, and their properties and interactions. Discovery of the Atom The earliest significant ideas to survive are due to the ancient Greeks in the fifth century BCE, especially those of the philosophers Leucippus and Democritus. They considered the question of whether a substance can be divided without limit into ever smaller pieces. There are only a few possible answers to this question. One is that infinitesimally small subdivision is possible. Democritus believed—that there is a smallest unit that cannot be further subdivided. Democritus called this the ATOM.  Alchemists discovered and rediscovered many facts but did not make them broadly available. As the Middle Ages ended, alchemy gradually faded, and the science of chemistry arose. It was no longer possible, nor considered desirable, to keep discoveries secret. An important fact was well established—the masses of reactants in specific chemical reactions always have a particular mass ratio.  The English chemist John Dalton (1766–1844) did much of this work, with significant contributions by the Italian physicist Amedeo Avogadro (1776–1856). The Austrian physicist Johann Josef Loschmidt was the first to measure the value of the constant in 1865 using the kinetic theory of gases. Dmitri Mendeleev (1834–1907), the great Russian chemist, proposed an ingenious array that highlighted the periodic nature of the properties of elements.  The first truly direct evidence of atoms is credited to Robert Brown, a Scottish botanist. In 1827, he noticed that tiny pollen grains suspended in still water moved about in complex paths. This can be observed with a microscope for any small particles in a fluid. The motion is caused by the random thermal motions of fluid molecules colliding with particles in the fluid, and it is now called Brownian motion. It was Albert Einstein who, starting in his epochal year of 1905, published several papers that explained precisely how Brownian motion could be used to measure the size of atoms and molecules.  Using Einstein’s ideas, the French physicist Jean-Baptiste Perrin (1870–1942) carefully observed Brownian motion; not only did he confirm Einstein’s theory, he also produced accurate sizes for atoms and molecules. A huge array of direct and indirect evidence for the existence of atoms now exists. For example, it has become possible to accelerate ions (much as electrons are accelerated in cathode-ray tubes) and to detect them individually as well as measure their Masses. The atom’s substructures, such as electron shells and the nucleus, are both interesting and important. The nucleus in turn has a substructure, as do the particles of which it is composed. Discovery of the Parts of the Atom: Electrons and Nuclei The Electron Gas discharge tubes, such as that shown in Figure, consist of an evacuated glass tube containing two metal electrodes and a rarefied gas. When a high voltage is applied to the electrodes, the gas glows. These tubes were the precursors to today’s neon lights.  They were first studied seriously by Heinrich Geissler, a German inventor and glassblower, starting in the 1860s. The English scientist William Crookes, among others, continued to study what for some time were called Crookes tubes. These “cathode rays” collide with the gas atoms and molecules and excite them, resulting in the emission of electromagnetic (EM) radiation. Gas discharge tubes today are most commonly called cathode-ray tubes, because the rays originate at the cathode.  The English physicist J. J. Thomson (1856–1940) improved and expanded the scope of experiments with gas discharge tubes. Thomson was also able to measure the ratio of the charge of the electron to its mass, qe/me—an important step to finding the actual values of both qe and me.  Figure shows a cathode-ray tube, which produces a narrow beam of electrons that passes through charging plates connected to a high-voltage power supply. These fields i.e, E and B, being perpendicular to each other, produce opposing forces on the electrons  𝑞𝑒 What is so important about , the ratio of the electron’s charge to its 𝑚𝑒 mass? The value obtained is 𝑞𝑒 11 𝐶 = −1.76 𝑥 10 (𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠) 𝑚𝑒 𝑘𝑔 This is a huge number, as Thomson realized, and it implies that the electron has a very small mass. It was known from electroplating that about 108 C/kg is needed to plate a material, a factor of about 1000 less than the charge per kilogram of electrons. Today, we know more precisely that 𝑞𝑝 7 𝐶 = 9.58 𝑥 10 ( 𝑝𝑟𝑜𝑡𝑜𝑛) 𝑚𝑝 𝑘𝑔  Thomson performed a variety of experiments using differing gases in discharge tubes and employing other methods, such as the photoelectric effect, for freeing electrons from atoms. He always found the same properties for the electron, proving it to be an independent particle. For his work, the important pieces of which he began to publish in 1897, Thomson was awarded the 1906 Nobel Prize in Physics. The Nucleus We examine the first direct evidence of the size and mass of the nucleus. Nuclear radioactivity was discovered in 1896, and it was soon the subject of intense study by a number of the best scientists in the world. Among them was New Zealander Lord Ernest Rutherford, who made numerous fundamental discoveries and earned the title of “father of Nuclear Physics.”  Rutherford’s experiment gave direct evidence for the size and mass of the nucleus by scattering alpha particles from a thin gold foil. Alpha particles with energies of about are emitted from a radioactive source (which is a small metal container in which a specific amount of a radioactive material is sealed), are collimated into a beam, and fall upon the foil. The number of particles that penetrate the foil or scatter to various angles indicates that gold nuclei are very small and contain nearly all of the gold atom’s mass. This is particularly indicated by the alpha particles that scatter to very large angles, much like a soccer ball bouncing off a goalie’s head.  Based on the size and mass of the nucleus revealed by his experiment, as well as the mass of electrons, Rutherford proposed the planetary model of the atom. The planetary model of the atom pictures low-mass electrons orbiting a large-mass nucleus.  Rutherford’s planetary model of the atom incorporates the characteristics of the nucleus, electrons, and the size of the atom. This model was the first to recognize the structure of atoms, in which low-mass electrons orbit a very small, massive nucleus in orbits much larger than the nucleus. The atom is mostly empty and is analogous to our planetary system. Summary As per gold foil experiment, Rutherford concluded that, There is positively charged center in an atom called NUCLEUS. All mass of atom resides in nucleus. The electron revolve around the nucleus in circular paths. The size of the nucleus is very small compared to the size of atom. Bohr’s Theory of the Hydrogen Atom The great Danish physicist Niels Bohr (1885–1962) made immediate use of Rutherford’s planetary model of the atom. Bohr became convinced of its validity and spent part of 1912 at Rutherford’s laboratory. In 1913, after returning to Copenhagen, he began publishing his theory of the simplest atom, hydrogen, based on the planetary model of the atom. Bohr’s theory explained the atomic spectrum of hydrogen and established new and broadly applicable principles in quantum mechanics. Mysteries of Atomic Spectra As we know that the energies of some small systems are quantized. Atomic and molecular emission and absorption spectra have been known for over a century to be discrete (or quantized). Maxwell and others had realized that there must be a connection between the spectrum of an atom and its structure, something like the resonant frequencies of musical instruments.  Part (a) shows, from left to right, a discharge tube, slit, and diffraction grating producing a line spectrum. Part (b) shows the emission line spectrum for iron. The discrete lines imply quantized energy states for the atoms that produce them. The line spectrum for each element is unique, providing a powerful and much used analytical tool, and many line spectra were well known for many years before they could be explained with physics.  The simplest atom—hydrogen, with its single electron—has a relatively simple spectrum. The hydrogen spectrum had been observed in the infrared (IR), visible, and ultraviolet (UV), and several series of spectral lines had been observed. The observed hydrogen-spectrum wavelengths can be calculated using the following formula: 1 1 1 =𝑅 2 − 2 , 𝜆 𝑛𝑓 𝑛𝑖 The diagram represents an Energy level diagram for hydrogen showing lyman, balmer and paschen series of transition.  where is the wavelength of the emitted EM radiation and is the Rydberg constant, determined by the experiment to be 107 𝑅 = 1.097 𝑥 𝑚 𝑜𝑟 𝑚−1 The constant nf is a positive integer associated with a specific series. For the Lyman series, nf =1 ; for the Balmer series, nf = 2; for the Paschen series, nf = 3; and so on. The Lyman series is entirely in the UV, while part of the Balmer series is visible with the remainder UV. The Paschen series and all the rest are entirely IR. There are apparently an unlimited number of series, although they lie progressively farther into the infrared and become difficult to observe as nf increases. The constant ni is a positive integer, but it must be greater than nf. Thus, for the Balmer series, nf =2 and ni = 3,4,5,6…….,. Bohr’s Solution for Hydrogen Bohr was able to derive the formula for the hydrogen spectrum using basic physics, the planetary model of the atom, and some very important new proposals. His first proposal is that only certain orbits are allowed: we say that the orbits of electrons in atoms are quantized.  Each orbit has a different energy, and electrons can move to a higher orbit by absorbing energy and drop to a lower orbit by emitting energy. If the orbits are quantized, the amount of energy absorbed or emitted is also quantized, producing discrete spectra. The energies of the photons are quantized, and their energy is explained as being equal to the change in energy of the electron when it moves from one orbit to another. In equation form, this is Δ𝐸 = ℎ𝑓 = 𝐸𝑖 − 𝐸𝑓 Here, Δ𝐸 is the change in energy between the initial and final orbits, and hf is the energy of the absorbed or emitted photon.  Figure shows an energy-level diagram, a convenient way to display energy states. In the present discussion, we take these to be the allowed energy levels of the electron. Energy is plotted vertically with the lowest or ground state at the bottom and with excited states above. Given the energies of the lines in an atomic spectrum, it is possible to determine the energy levels of an atom. Triumphs and Limits of the Bohr Theory He explain the spectrum of hydrogen, he correctly calculated the size of the atom from basic physics. Some of his ideas are broadly applicable. Electron orbital energies are quantized in all atoms and molecules. Angular momentum is quantized.  But there are limits to Bohr’s theory. It cannot be applied to multi electron atoms, even one as simple as a two-electron helium atom. Bohr’s model is what we call semiclassical. The orbits are quantized (nonclassical) but are assumed to be simple circular paths (classical). Bohr’s theory also did not explain that some spectral lines are doublets (split into two) when examined closely. 1. Which of the following electron transitions will emit a photon in visible light spectrum? A. n=5 to n=3 B. n=5 to n=1 C. n=4 to n=2 D. n=6 to n=4 THANK YOU