Chemistry 163A Problems: Uncertainty Principle, Rydberg Constant, and Quantum Operators, Assignments of Quantum Mechanics

Download Chemistry 163A Problems: Uncertainty Principle, Rydberg Constant, and Quantum Operators and more Assignments Quantum Mechanics in PDF only on Docsity! CHEMISTRY 163A PROBLEMS (6) (a) What is the minimum uncertainty in velocity for an electron in a 1s orbital in a hydrogen atom (assume the electron is confined to a linear region 2ao)? If the average velocity of the 1s electron is 2.19 x 106 m s-1, what is the fractional uncertainty? (b) In parking a 2 × 103 Kg automobile you are moving with an uncertainty in velocity of 0.1 m/sec. What is the uncertainty in position? What fraction of the width of a 10 m parking space is this? Is it likely that you can blame the wave-like properties of matter for the scratch you put on the car when parking? (7) From the handout on evaluating the Rydberg constant using the correspondence principle: (a) Briefly, what is the correspondence principle? (b) Qualitatively, under what conditions (with regard to energy) should νqm = νcl? (c) Quantitatively, under what limits for νqm will νqm → νcl, i.e., in the correspondence limit how does νqm depend on R and n? (8) For the operator  d d = +h i φ (a) Which if the following are eigenfunctions: (i) cos mφ (ii) sin mφ (iii) exp(imφ) (iv) exp(–imφ) (b) For any of the examples in (a) which are eigenfunctions what are their respective eigenvalues? (c) What is ( ˆ )A 2 ? (d) Which of the functions in part (a) are eigenfunctions of ( ˆ )A 2 and what are their respective eigenvalues? (9) Find normalization constants for the following functions: (a) sin 2 x L π    in ( 0, L ) (b) xe x 2− in −∞ ∞( ), (10) McQ. #4-2 *(11) McQ. #3-6