Chapter 29 Molecular and Solid-State Physics

Size: px

Start display at page:

Download "Chapter 29 Molecular and Solid-State Physics"

Shannon Bailey
5 years ago
Views:

1 Chapter 29 Molecular and Solid-State Physics GOALS When you have mastered the content of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms, and use each term in an operational definition: ionic bonding extrinsic semiconductor covalent bonding semiconductor fluorescence superconductivity phosphorescence nuclear magnetic resonance bioluminescence Band Theory of Solids State the band theory of solids, and use it to explain the optical and electrical properties of different solids. Molecular Absorption Spectra Explain the basis of vibrational and rotational absorption spectra of molecules. Solid-State Problems Solve problems involving vibrational and rotational energy states of molecules and the band theory of solids. PREREQUISITES Before beginning this chapter you should have achieved the goals of Chapter 21, Electrical Properties of Matter, Chapter 27, Quantum and Relativistic Physics, and Chapter 28, Atomic Physics. 239

2 Chapter 29 Molecular and Solid-State Physics OVERVIEW Investigation has shown that there are basically four types of bonding which hold atoms together in solids; ionic, covalent, Van der Walls, and metallic bonding. These bonding models are primarily electrical in nature and predetermine many of the macroscopic properties observed in solids. These properties include hardness, chemical activity, electrical activity, thermal activity, and boiling point. In this chapter you will be introduced to several general properties of solids and to applications which utilize these unique characteristics. SUGGESTED STUDY PROCEDURE Start your study of this chapter by reading these Chapter Goals: Definitions, Band Theory of Solids, and Molecular Absorption Spectra. An extended discussion of many of the terms listed under the Definitions goal are provided in the first section of this Study Guide chapter. Next, read text sections As you read sections 29.4 and 29.3, please note the simplistic nature of the "dumbbell" model and the influence of the quantum nature found in the expressions for E vib and E rot. Questions which you encounter in reading are answered in the second section of this Study Guide chapter. Now turn to the end of the chapter and read the Chapter Summary and complete Summary Exercises 1-9. Next, do Algorithmic Problems 1 and 2 and Exercises and Problems 1 and 2. For more work with the concepts introduced in this Study Guide chapter, work through the problems given in the Examples section of this Study Guide chapter. Now you should be prepared to attempt the Practice Test located at the end of this Study Guide chapter. If you have difficulty with any part of the test, refer back to a specific text section or to this for further assistance. This study procedure is outlined below Chapter Goals Suggested Summary Algorithmic Exercises Text Readings Exercises Problems & Problems Definitions 29.1,29.2,29.3, 1-6 1,2 29.6,29.7, , 29.16, Band Theory of 29.8,29.9,29.10, 7 Solids 29.11,29.12, Molecular 29.4,29.5, ,9 1,2 Absorption Spectra Solid State 29.4, ,11 3,4 4,5,8 Problems 240

3 DEFINITIONS IONIC BONDING - Attractive force between positive and negative ions makes a strong bond for ionic materials like Na+ Cl-. To gain some appreciation for the size of the electric forces in ionic materials remember that the largest electric fields in your usual environment are on the order 10 4 V/m near high voltage transmission lines. The electric fields in ionic materials are a million times larger than those, i.e V/m. COVALENT BONDING - The bond produced by shared electrons between atoms making up covalent systems, e.g., H 2. Compounds studied in organic chemistry are primarily covalent materials in which the carbon-hydrogen covalent bonding is most prevalent. FLUORESCENCE - The light emitted by a substance while it is irradiated. Fluorescent light has longer wavelength than incident light and ceases when incident light is removed. The common fluorescent light fixture makes use of this phenomena for producing visible light. PHOSPHORESCENCE - Characterized by light emitted after incident radiation is removed from the source material. The various glow-in-the-dark objects are examples of phosphorescent materials. BIOLUMINESCENCE - Certain biological systems produce light as a consequence of their biochemical processes. The cool light emitted by insects such as fireflies is a common example of bioluminescence. EXTRINSIC SEMICONDUCTOR - A semiconductor that has been doped with a donor material (n type) or an acceptor material (p type). A donor is thought of as an element with one more electrons in its outer most electron shell than the host semiconductor. An acceptor is an element which one less electron in its outer most electron shell than the host semiconductor. Look at a periodic table (at the back of the text) and list the elements that will act as acceptors in germanium or silicon, as donors. SEMICONDUCTOR - A material whose room temperature electrical conductivity (σ 1 ohm -1 m -1 ) is much greater than the conductivity of insulators ((σ ohm- ohm -1 m -1 ) and much less than the conductivity of the good metallic conductors ((σ 10 4 ohm -1 m -1 ). SUPERCONDUCTIVITY - The phenomena characterized by materials that show resistivity going to zero at a critical temperature between absolute zero (O ø K) and 80 ø K. It is possible to construct a model of superconductivity which predicts the existence of room temperature superconductors, but no one has found one yet. 241

4 NUCLEAR MAGNETIC RESONANCE - The phenomena characterized by energy level resonance associated with the proton magnetic dipole in materials. The extreme sensitivity of detection systems making use of resonance have made such systems common in the basic research laboratories around the world. ANSWERS TO QUESTIONS FOUND IN THE TEXT SECTION 29.1 Introduction In Chapter 28 we developed a nuclear model to explain the properties of atoms. If we put many atoms close together to form a solid object what aspects of our atomic model will we need to change? How will photons of light interact with atoms closely packed together in solids? Presumably the transition by electrons from one energy level to another will result in the emission or absorption of photons. SECTION 29.8 Solids Ionic bonding would seem to lead to the formation of light, brittle solids. The weaker bonding mechanisms should allow for softer, more pliable solids. Stainless steel is an alloy especially developed for use where a strong metal which would not rust is required. SECTION Conductors Question - 1. In a conductor there are always electrons free to move in the conduction band. These electrons can move in response to any energy gradient, either electrical or thermal. Hence, materials which are excellent electrical conductors would also be good thermal conductors. The best specific example is silver. SECTION Intrinsic Semiconductors Question - 2. Intrinsic semiconductors have a band gap of the order of 1eV. Visible light has an energy of the order of 2eV. The photons of visible light can be absorbed by electrons in the valence band of semiconductors and lifted into the conduction band. Hence we predict that intrinsic semiconductors will be opaque to visible light and will conduct electricity readily while exposed to bright visible light. EXAMPLES MOLECULAR ABSORPTION SPECTRA 1. The vibrational and rotational lines of the molecule HCl are found at about λ = 3.3 x 10-4 cm. (a) What is the force constant for the vibrational motion of HCl? (b) What is the moment of inertia of HCl? (c) What are the splittings we could expect between the various quantum levels for vibrational and rotational spectra in ev? (d) What are the splittings (in ev) we could expect between the HCl 35 lines and the HCl 37 lines? What data are given? The HCl molecule has ground state vibrational and rotational energy levels at λ= 3.3 x10-4 cm = 3.3 x10-6 m = 3,300 nm. 242

5 What data are implied? Natural occuring chlorine occurs with two different masses, one Cl 35 has a gram molecular mass of 35 gm and the other Cl 37 has a gram molecular mass of 37 gm. The natural abundances gives chlorine an average gram molecular mass of 35.5 gm. What physics principles are involved? The properties of rotating and vibrating quantum mechanical systems as discussed in Sections 29.4 and 29.5 of the textbook. What equations are to be used? E vib = (n + 1/2)(h/2π)(k/m) 1/2, where m = (M 1 M 2 ) / (M 1 + M 2 ) (29.2) E rot = J(J + 1)(h/2π) 2 (1/2I) (29.3) Solutions (a) Use an average mass for chlorine; M 2 = 35.5, then m HCL ((1)(35.5)/( )) x 1.66 x kg = 1.61 x kg Eo hc/λ o = (1/2)(h/2π) x SQR RT(k/1.61 x ) (3 x 10 8 m/s) / (3.3 x 10-6 m) = 1/(4π) x SQR RT(k/1.61 x ) 11.4 x /s = SQR RT(k/1.61 x ) 1.30 x = SQR RT(k/1.61 x ) 2.1 x 10 3 N/m = k, the force constant for H Cl. (b) E rot hc/λ o 1(h/2π) 2 x (1/2I) C / λ o = h / (8π 2 I) (3.0 x 10 8 m/s) / (3.0 x 10-6 m) = (6.63 x J S) / (8π 2 I) I = 9.2 x10-50 kg m2 (c) Ground State Energy = hc/λ o = ((6.63 x )(3.0 x 10 8 )) / 3.3 x 10-6 E o = 6.03 x10-20 J = 0.377eV For vibrational levels the levels are evenly split, so E o = E vib (½)hf; ΔE o = hf = 2E o energy splittings for vibration states 2E o 0.75eV For rotational states the splittings change Say J = 0 to J = 1 transition is Eo Then J = 1 to J = 2 transition is 2Eo and J = 2 to J = 3 transition is 6Eo and so on. (d) The effective mass of the molecule changes slightly m 35 /m 37 = [((1)(35))/(1+35)) / ((1)(37)/(1+37))] m 35 /m 37 = / = 99.85% Thus the E vib would change by less than 15 parts in 10,

6 PRACTICE TEST 1. Distinguish between the following terms: a) Florescence b) Phosphorescence c) Illuminescence 2. Use the band theory of solids to explain how a pure, intrinsic semiconductor (like germanium) can become a p-type semiconductor. Your explanation should utilize a diagram showing the details of the band theory. 3. The energy levels predicted for a molecule are as follows: E vib = (n + 1/2) (h/2π)(k/m) 1/2 (vibrational) E rot = J (J + 1) (h/2π) 2 /2I (rotational) a) Describe the mechanical model used to formulate each of these mathematical models. b) Identify the important parts of each of the mathematical models. ANSWERS: 1. a) Excited molecule gives up some of its energy through vibrational contact with other molecules. In a lower energy state, the molecules then emit a photon (longer l) to return to a ground state. b) Molecules involved are excited and return to the ground state through an intermediate state with a long lifetime. These molecules then emit photons at various times to return to the ground state. This slow nature gives a characteristic "afterglow." c) The emission of light due to the excitation of electrons. Lasers and light-emitting diodes used in calculators are examples of illuminescence A pure semiconductor when doped with a substance that has one less electron than the semiconductor gains acceptor states or holes in the forbidden gap region near the valence band. Electrons from the valence band can then move into the acceptor states (by tunneling or by increased thermal energy) where they are trapped. 3. a) The molecule is like a dumbbell with a spring connecting each atom. b) h - planck's constant k - effective spring constant m - effective mass of the system n - quantum no. for vibration J - quantum no. for rotation I - moment of inertia 244

Modern Physics for Frommies IV The Universe - Small to Large Lecture 4

Fromm Institute for Lifelong Learning University of San Francisco Modern Physics for Frommies IV The Universe - Small to Large Lecture 4 3 February 06 Modern Physics IV Lecture 4 Agenda Administrative