Physics 215 Winter 2002 Introduction to Modern Physics Prof. Ioan Kosztin May 13, 2001 Final Exam This is a closed book exam. During the exam, you may only use a simple pocket calculator. The duration of the exam is 2 hours. Provide a one paragraph answer to the following questions: 1. [10pt] What is the difference between an intrinsic and an extrinsic semiconductor? 2. [10pt] In what consist the normal and anomalous Zeeman effect? 3. [10pt] What are Hund’s rules and how do they apply? 4. [10pt] What are the features and shortcomings of the Bohr atom model? 5. [10pt] What is the physical meaning of the Pauli exclusion principle? 6. [10pt] What do describe the Fermi-Dirac and Bose-Einstein statistics? Solve the following problems: 7. [10pt] Sodium is a monovalent metal having a density of 0.971 g/cm3 and a molar mass of 23.0 g/mol. Use this information to calculate (a) the density of charge carriers, (b) the Fermi energy, and (c) the Fermi speed for sodium. Hint: The relationship between the number density (i.e., n=N/V) of the conduction electrons in a metal and the corresponding Fermi momentum is given by 333082.(2 ) 3FpFdp pnhππ==∫= 8. [10pt] A mystery particle enters the region between the plates of a Thomson apparatus as shown in Figure 1. The deflection angle θ is measured to be 0.20 radians for this particle when V= 2000 V, ℓ = 10.0 cm, and d = 2.00 cm. If a perpendicular magnetic field of magnitude B =4.57 X 10-2 T is applied simultaneously with the electricPhysics 215 Final Exam - 2 - field, the particle passes through the plates without deflection. (a) Find q/m for this particle. (b) Identify the particle. (c) Find the horizontal speed with which the particle entered the plates. Figure 1 Deflection of negative particles by an electric field. 9. [10pt] An electron is described by the wavefunction 0for0()(1 ) for 0xxxxCe e xψ−−<=−> where x is in nanometers and C is a normalization constant. (a) Find the value of C that normalizes ψ. (b) Where is the electron most likely to be found; that is, for what value of x is the probability for finding the electron largest? (c) Calculate x (i.e., the average value of the x coordinate) for this electron and compare your result with its most likely position. Comment on any differences you find. 10. [10pt] From the optical absorption spectrum of a certain semiconductor one finds that the longest wavelength of radiation absorbed is 1.85 µm. Calculate the energy gap (in eV) for this semiconductor.Physics 215 Final Exam - 3 - Useful physical constants: electron mass: m=9.1x10-31 kg elementary charge: e=1.6x10-19 C Planck’s constant: h=6.62x10-34 Js Speed of light: c=3x108 m/s Avogadro’s number: 6.02x1023