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Unformatted text preview: 23 January, 2006 Michael F. Brown
CHEMISTRY 481 (Biophysical Chemistry) Problem Set 02 To be turned in by: Monday, 30 January Worked examples for this course are dealt with primarily in the Discussion Section; whereas new
concepts are introduced in the Lectures. You can get help with the homework problems in the
Discussion Sections (12:30—13:20 Tues, Koefﬂer 216; and 13:00—13:50 Wed, Koefﬂer 216).
The problem sets will be graded P+, P, or F and will be used to increase or decrease borderline
grades. On all computational problems be sure to use SI units, and indicate your answer to the
proper number of significant figures. For maximum credit show clearly how you obtained your
answer, i.e. what numbers were combined to yield the final result. Background reading: Atkins & de Paula, Chapters 11 and 12
Examples and exercises related to the homework (optional): Back of Chapter Exercises: 11.8, 11.11, 11,14, 11.17, 11.19, 12.4, 12.5
Back of Chapter Problems: 11.4, 12.1 Problem 1. Being good sports let us consider the familiar (although mysterious!) hydrogen
atom. The excited state wavefunction corresponding to a hydrogenic 2s orbital is given by m a 0 we): 1 [2—LJ6_r/2ao where the Bohr radius a0 = 52.9 pm.
a) Find the normalized wavefunction.
b) Estimate the probability that an electron is in a volume 1: = 1.0 pm3 at the nucleus (r = O). c) Estimate the probability that an electron is in a volume 1: = 1.0 pm3 in an arbitrary direction at
the Bohr radius (r = a0). (1) Estimate the probability that an electron is in a volume 1: = 1.0 pm3 at infinity (r = 00). Problem 2. Consider a hydrogen atom in its ground state, for which the wave function
(normalized) is: 1 e—r/a0 WU) = 3
Ilia
0 where a0 = 52.9 pm is the Bohr radius. Find the root mean square distance <r2>“2 of the
electron from the nucleus, in which < > denotes the expectation value. Problem 3. Let us consider two of the excited state wavefunctions for the hydrogen atom: a) Normalize the following wavefunction to unity:
2 _ I“ —r/ a
1P (r) = —— e 0 a b) Normalize the following wavefunction to unity: 1p (r) = rsinB cos (1,) e_r/2ao Problem 4. You are a theoretical Quantum Chemist interested in the electronic properties of conjugated polyenes. The groundstate wavefunction for a particle in a onedimensional box
of length L is: w (x) = 3 sin
L L Assume that the box is 10.0 nm long. a) Calculate the probability that the particle is between x = 4.95 nm and 5.05 nm: b) Calculate the probability that the particle is between x = 1.95 nm and 2.05 nm: c) Calculate the probability that the particle is between x = 9.90 and 10.00 nm: d) Calculate the probability that the particle is in the right half of the box: e) Calculate the probability that the particle is in the central third of the box: 01 2306
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 Spring '06
 brown
 Physical chemistry, pH

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