Exam 1 Questions with Crib Sheet - Physical Chemistry | CHEM 455, Exams of Physical Chemistry

Download Exam 1 Questions with Crib Sheet - Physical Chemistry | CHEM 455 and more Exams Physical Chemistry in PDF only on Docsity! C455A –Quantum Chemistry and Spectroscopy Exam 1 April 26, 2004 Exams will be collected at 9:30:00 am SHARP 1 8.5x11” page of notes is allowed -ALL ANSWERS MUST BE IN THE ANSWER BOX -CROSSED OUT/PARTIALLY ERASED WORK WILL BE IGNORED -NO PARTIAL CREDIT ON NUMERICAL PROBLEMS WITHOUT A FORMULA -NO PARTIAL CREDIT ON “PHYSICALLY IMPLAUSIBLE” ANSWERS UNLESS THE ERROR IS RECOGNIZED Your name:____________________________________________ Student ID#:___________________________________________ I have neither received not provided assistance of any kind on this exam. Signature:___________________________________________ Total Points: 100 Question 1:_________/16 Question 2:_________/35 Question 3:_________/13 Question 4:_________/36 Total: _____________/ Potentially Useful Information: Workfunctions of Metals: Li 2.3 eV Ca 2.87 eV Al 4.28 eV Au 5.1 eV 2-continued 2) 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 should assume all lines continue to infinity in their present functional shapes. If any question is not possible to determine with the information provided then explain why not. 2a) In which potential will the electron have the smallest zero point (ground state) energy? Explain/interpret your answer. 2b) In which potential is the probability of finding the electron at x=0 going to be the largest? Explain. How would you calculate the probability of finding the particle between x=-infinity and x=0 in this potential? (write down an expression for this probability as an integral, calling the wave function ψ). Evaluate this integral (it shouldn’t require a lot of math) to find the probability. 2b: potential # 2b: probability= 2a: potential # 2c) For which potential could we find solutions to the time-independent Schrödinger equation that correspond to an electron with a well defined momentum? Explain, including an equation showing what the wave-function of a particle with a well defined momentum (value of +d) would be. 2d) Show, by explicit application of the x-momentum operator, px , that the wavefunction you wrote down in equation 1c is an eigenfunction of the operator px. What is the eigenvalue? 2e) If the units on the x-axis of the graphs are in nanometers, what energy (in eV) of photon would be needed to excite an electron from the ground to the first excited state in potential ii ? 2e: Problem 3 (14 points) (For the problems below, assume that all photoelectrons that could possibly be emitted are emitted, and that 100% of these emitted electrons are measured as a current). 3a) What is the photocurrent (in Amps) that would be expected if 1 µW of power from the 458 nm line of an Ar+ laser was directed at a photocathode made of Lithium? 3b) What is the photocurrent (in Amps) that would be expected if 1 mW of power from the 325 nm line of an HeCd laser was directed at a photocathode made of Gold? Problem 4 (36 points) 4) A particle is placed in a potential of the form: 2 2 1)( bxxV = in a state where the wave function of the particle, φ, is given by the equation: ))(31(2)( 7531 ψψψψφ ii −+++= (Here ψn represents the nth normalized energy eigenfunction of a Harmonic Oscillator with spring constant b, and energy En as given by the formula for a harmonic oscillator) ))(31(2)( 7531 ψψψψφ ii −+++= (repeated here for your convenience) 3a: 3b: