Quantum Chemistry and Spectroscopy Exam 1: Topics in Quantum Mechanics and Spectroscopy, Exams of Physical Chemistry

Download Quantum Chemistry and Spectroscopy Exam 1: Topics in Quantum Mechanics and Spectroscopy and more Exams Physical Chemistry in PDF only on Docsity! Quantum Chemistry and Spectroscopy Exam 1 Oct. 22, 2003 Exams will be collected at 10:20:00 am sharp Open Book and Open Notes -ALL ANSWERS MUST BE CIRCLED -CROSSED OUT/PARTIALLY ERASED WORK WILL BE IGNORED -NO PARTIAL CREDIT ON NUMERICAL PROBLEMS WITHOUT A FORMULA Your name:____________________________________________ Student ID#:___________________________________________ Signature:___________________________________________ Total Points: 100 Question 1:_________/10 Question 2:_________/15 Question 3:_________/25 Question 4:_________/32 Question 5:_________/10 Question 6:_________/8 Total: _____________/100 Useful Information: Workfunctions of Metals: Li 2.3 eV Ca 2.87 eV Al 4.28 eV Au 5.1 eV (25 Points) 3) An electron is placed into each of the following 1-D potential wells (i.e. the y-value represents the potential as a function of position along the x-axis): i) ii) iii) a) V(x)=0.75 c) V(x)=0.75 b) V(x)=0 3-continued 3) An electron is placed into each of the 1-D potential wells on the previous page, the axes labels are in arbitrary units, but are the same scale for each graph. You may assume all lines continue to infinity in their present functional shapes. 3a) In which potential will the electron have the smallest zero point energy? Explain/interpret your answer. 3b) In which potential will the electron have the fewest bound state wavefunctions? (if it not possible to determine with the information provided then explain why not). Explain. 3c) In which potential is the probability of finding the electron at x=0 going to be the highest? How would you calculate the probability of finding the particle between x=0 and x=+infinity (write down an integral calling the wave function ψ). What would the answer be for this potential (you shouldn’t need to perform a calculation)? 3d) Write down the time-independent Schrödinger equation for potential (iii) and the functional form of the solutions to the time-independent Schrödinger equation for potential (iii) in each of the regions (a), (b) and (c) 3e) What four conditions must you impose on a wave function to obtain a physically valid solution to the Schrödinger equation? Explain how you would use these conditions to obtain the undetermined coefficients in d) (you need not calculate complicated derivatives, but you must explain what needs to be done) (10 Points) 5) A particle is in the state: ψ = e-idx where d is a constant. a) Is this state an eigenfunction of the momentum operator, px? (prove your answer) b) What is the physical interpretation of this state? c) What can you say about the position of this particle? (8 Points) These are questions from the P-chem section of old GRE exams: (CIRCLE THE CORRECT ANSWER) 6) The presence of a weak band in the infrared absorption spectrum of HCl gas at a frequency roughly twice that of the strong fundamental band can be ascribed to: a) the presence of different isotopes of chlorine in HCl b) transitions from the n=1 to the n=2 vibrational state c) transitions from the n=0 to the n=2 vibrational state d) changes in electronic energy e) changes in rotational energy The energy of which of the following systems is NOT quantized: a) a particle in a box b) a particle in free space c) electrons in the hydrogen atom d) a simple harmonic oscillator e) a particle on a ring In comparison with HCl, the frequency for the transition of DCl from the ground vibrational state to the first excited vibrational state is: a) higher for DCl b) lower for DCl c) sometimes higher and sometimes lower for DCl depending on the temperature and concentration d) the same for both DCl and HCl e) not determinable Which of the following wave number corresponds to energy in the infrared region of the electromagnetic spectrum? a) 1,700,000 cm-1 a) 100,000 cm-1 a) 33,000 cm-1 a) 20,000 cm-1 a) 2,000 cm-1