Exam questions

Two of the four questions on the written exam will come from the left column. A green number or bullet point indicates that a solution is available.

Left column: Potential exam questions	Right column: Practice questions
1. Molecules Hydrogen wavefunction Probability of finding an electron Energy of an approximate wavefunction Molecular orbitals - Exam January 2010 Absorption in 1,3-butadiene Lithium wavefunction - Exam May 2011 Carbon monoxide - Exam March 2011 Infrared radiation absorbed by a quantum dot Nitrogen - Exam June 2011 The questions without numbers will not be discussed during the exercise sessions Many electron wave function Hamiltonian matrix Valence bond theory - Exam April 2010 Molecular orbitals of H₂ - Exam October 2010 MIT 8.231 Problem 2.7, sp² Hybridization Bond angle- Exam January 2012	Butadiene - Exam June 2010 Beryllium wavefunction The Morse potential Singlet - triplet splitting Estimate the size of an atom Variational wavefunction Water molecule Molecular orbitals of methane - Exam October 2011
2. Crystal structures Copper oxide - Exam April 2009 Graphene Two-dimensional Wigner-Seitz cell Metal density - Exam November 2008 Arrangement of atoms on the surface of a crystal ≈ Exam March 2008 ≈ Exam October 2009 Primitive unit cell of fcc Draw the hkl plane Equivalent planes and directions - Exam January 2012 The crystal structure of SrTiO₃ The angle between the [110] direction and the [111] direction - Exam October 2011 MIT 8.231 Problem 1.7, Graphite Conventional unit cell - Exam October 2010 A C-centered tetragonal Bravais lattice does not exist The distance between nearest neighbor atoms - Exam November 2009 MIT 8.231 Problem 1.1, Gallium Arsenide MIT 8.231 Problem 1.2, Calcium Fluoride MIT 8.231 Problem 1.6, Packing Fraction Atomic packing density	Oral exam questions about crystal structures Metal density Which planes are equivalent to (100) in a tetragonal system? Kittel 1.3: Hcp structure Wigner-Seitz Cell Two-dimensional crystal - Exam May 2011 Packing density in the hcp structure Orthorhombic crystal- Exam July 2009
3. Crystal diffraction Find the reciprocal lattice of a monoclinic crystal The Fourier transform of a two-dimensional function Determine the fourier transform of a periodic function Interference of scattered x-rays Ewald sphere Form factor for atomic hydrogen A two-dimensional crystal Structure factor Powder diffraction Single crystal diffraction - Exam January 2011 Reciprocal lattice of a tetragonal crystal - Exam January 2010 Diffraction, Exam question 2 - June 10, 2008 Bragg diffraction MIT 8.231 Problem 2.1, Americium MIT 8.231 Problem 2.4, Reciprocal lattice of conventional versus primitive unit cells MIT 8.231 Problem 2.5, Indium Diffraction using a free electron laser - Exam October 2009 Protein structure - Exam April 2009 Bragg law - Exam November 2009	Some oral exam questions about diffraction Bragg diffraction Reciprocal lattice of fcc Rhombohedral unit cell Fourier series in 3 dimensions Exam question 1 - March 11, 2008 Diffraction experiments Powder diffraction Reciprocal lattice Diffraction from a quartz crystal Bragg's law - Laue condition Structure factors of a two-dimensional function The structure factor of a simple cubic crystal Reciprocal lattice of fcc - Exam March 2011 Determine the fourier transform of a periodic function
4. Crystal binding Ionic bonding in NaCl Madelung constant for a 2D ionic crystal Van der Waals crystal Compressibility of NaCl Electrostatic bond The Lennard-Jones potential Ionic crystal, Exam April 2010 Ibach and Lüth 1.3 - Solubility of NaCl Madelung constant of CsCl Ibach and Lüth 1.5 - Ionic crystals Chemical bonds in solids - Exam November 2008	Madelung constant for a 1-d chain
5. Photons Density of states Energy spectral density in 1-D Exam May 2011 Relationship between photons and phonons	Ibach and Lüth 5.1 - 1-d and 2-d elastic continuum Oral exam questions about photons
6. Lattice vibrations and phonons Wavevectors in a one-dimensional chain Length of the largest wave vector Phonon dispersion, Exam April 2008 Phonons in a 1-d chain Eigenfunctions of the translation operator Counting phonons Kittel 6.1: Heat capacity of a one-dimensional lattice Kittel 4.3: Basis of two unlike atoms Hall problem 2.3 MIT 8.231 Problem 4.3, Two-dimensional Debye model Phonon dispersion, Exam March 2008, Exam June 2011 Cesium Chloride, Exam June 2008 Cesium Iodine Exam July 2010	Oral exam - phonons Continuum wave equation Einstein model - Exam January 2009 Vibrations of a square lattice
7. Free electron gas The Fermi energy of a metal - Exam June 2008 Heat capacity of electrons in 2-d Thermodynamic properties of a metal Sommerfeld expansion Diffusive charge transport in aluminum Thermal conductivity Density of states D(k) Gold - Exam October 2010 Kittel 6.2: Pressure and bulk modulus of an electron gas Sommerfeld expansion - Exam June 2008	The Fermi energy of a metal Average electron energy in a metal Ibach and Lüth 7.1 - Friedel oscillations Chemical potential of a metal - Exam May 2011 Average electron energy in a metal - Exam June 2010 MIT 8.231 Problem 5.3, Chemical potential of a two-dimensional electron gas
8. Energy bands One dimensional potential Empty lattice approximation- Exam November 2009 Calculate E_F - Exam March 2008, Exam June 2011 Kittel problem 9.4: Square lattice, free electron energies Tight binding Band structure - Exam June 2010 Fermi energy of aluminum - Exam March 2011 Empty lattice approximation Central equations Tight-binding model - Exam January 2012	Calculate the Fermi energy Empty lattice approximation - Exam January 2009 Empty lattice approximation - Exam October 2011 Metal, semiconductor, insulator - Exam October 2009 Band structure - Exam June 2009
9. Crystal physics Point groups Elastic deformation Point group notation Pyroelectricity - Exam January 2011 How do you calculate thermodynamic properties? - Exam October 2011	Pyroelectricity Mirror planes NaCl - Exam January 2009 Piezoelectricity Thermal expansion Oral exam questions about crystal physics
10. Semiconductor Physics Effective mass, Exam April 2008, Exam January 2009, Exam July 2010 Conduction band electron energy - Exam October 2010 Chemical potential of a semiconductor - Exam November 2008 Chemical potential of Ge - Exam April 2009 Fermi energies in extrinsic semiconductors - Exam November 2009 Hall effect Donors in GaAs Conductivity of a semiconductor GaAs - Exam January 2011 Fermi energies in intrinsic semiconductors Chemical potential of a semiconductor - Exam January 2012 Hole concentration in intrinsic silicon Carriers in a doped semiconductor - Exam April 2008	Oral exam questions about semiconductors Oral exam - Effective mass The depletion approximation for a pn junction Dopant separation Ionized donors Maximum field strength in a pn junction pn - junction, Exam April 2010 Refrigeration with semiconductors Carrier generation
11. Magnetism Paramagnetism in potasium Ferromagnetism - Exam June 2008 Magnetism - Exam January 2011 Mean field theory - Exam July 2010, Exam July 2011	Oral exam questions about magnetism Hard and soft magnets - Exam March 2011 Ferrimagnetism - Exam April, 2009 Bloch wall - Exam January 2010







513.001 Molecular and Solid State Physics