Homework is due a week after it is assigned, usually on Tuesdays, and can be
turned in at the lecture room or by
Answers are posted in the Leigh Hall ground floor, North side corridor.
Exercises (Ex.) and problems (Pr.) are taken from Atkins and dePaula' book,
8th edition, and may have modified data. Chapter numbers are for the combined
volume , starting with Chap. 8 (Quantum Theory: introduction and
principles). This is the first chapter
of volume 2. Each problem is worth 5
points.
SHOW YOUR MATHEMATICAL DERIVATIONS
FRAME ALL FINAL ANSWERS. USE SI UNITS EXCEPT AS REQUIRED.
Useful sources of physical and chemical data: http://webbook.nist.gov/chemistry, NIST Constants and Units, NIST Physics Data
Useful mathematics tutorials and software: Mathematica , Maple , MATLAB
Atkins-dePaula web resources at http://bcs.whfreeman.com/pchem8e
Read Appendices 2 and 3, and Chapter 8, secs. 8.1 to 8.4.
Homework 1 (Due on Tuesday, January 13; each exercise from chap. 8)
1) Given the complex numbers z_j= x_j + i y_j , j=1,2, (a) express z_1/z_2 in terms of their real and imaginary parts, and (b) give the polar form of each number as z= A exp(i alpha) and the quotient in (a) from real and imaginary parts; 2) Ex. 8.1a, but for a wavelength of 2.0 nm; 3) Ex. 8.4a; 4) Ex. 8.9a but for (a) 2.0 fs; (b) 20 fs; (c) 0.5 s; 5) Problem 8.1 but for the sunlight temperature of 5,800 K (see the spectrum (jpg file) : solar spectrum ); 6) Probl. 8.4, only for (a), and a box of length 15.0 nm; 7) Probl. 8.14; 8) For extra credit, give an upper bound to the probability that Schroedinger’s cat is both dead and alive when observed for 10 s if the difference of energies for alive (a) and dead (d) states is 500 kJ.
Read Chapter 8, and Chap. 9, secs. 9.1 to 9.5.
Homework 2 (Due on Tuesday, January 20; each exercise from chap. 8 or 9)
1) Ex. 8.12a, also when the bullet has the mass of a proton; 2) Probl. 8.20, only (a) and (b); 3) Ex. 9.1a but for a box of length 2.0 nm; 4) Ex. 9.3a but for the state n=2; 5) Ex. 9.10a but for a force constant of 313 N/m.
Read Chapter 9.
Homework 3 (Due on Tuesday, January 27)
1) Using the figure 9.45 in Problem 9.5, (a) sketch the lowest eigenfunction of energy E < epsilon (ground state), and the lowest with energy E > epsilon (first excited state), and also (b) give expressions for the deBroglie wavelengths on top of the step and on its sides in terms of E, epsilon, and the mass m; 2) Probl. 9.32; 3) Probl. 9.20, only (a) and (c); 4) Probl. 9.3 for excitation energies from ground to first and also from ground to second excited states; 5) Ex. 9.18a; 6) Probl. 9.23, only (b).
Read Sections10.1 to 10.5.
Homework 4 (Due on Tuesday, February 3)
1) Solve self-test 10.3 by drawing a plot and finding its intercepts and slope; 2) Ex. 10.3a giving answers in pm; 3) Ex. 10.5a, and compare the results; 4) Ex. 10.8a, for radial nodal points, and angular nodal planes; 5) Ex. 10.11a; 6) Ex. 10.10a; 7) Ex. 10.14a, and mention which rule applies in each case; 8) Write acceptable singlet and triplet wavefunctions for He(1s2p_z), with spin projection quantum number M_S=0.
Read Sections10.6 to 10.9, and Chap. 11, sections 11.1 and 11.2.
Homework 5 (Due on Tuesday, February 10)
1) Ex. 10.15a but for Ni^{+3}; 2) Ex. 10.17a; 3) Ex. 10.18a; 4) Problem 10.6, list the involved atomic terms, and give the level splitting in wavenumbers; 5) Compare the velocity of a proton to that of an electron in a H1s orbital using that the kinetic energy of H1s is 13.598 eV for (a) a proton beam with kinetic energy of 1.0 eV, (b) a proton beam with kinetic energy 1.0 MeV, and indicate whether the Born-Oppenheimer approximation is valid in each case; 6) Give the three wavefunctions for the lowest energy triplet of H_2 from valence-bond (VB) theory and using 1s orbitals; 7) Using VB theory, give the electron pair wavefunctions for the bonds of C_2 from 2p orbitals, and also its lone pair wavefunctions from 2s orbitals .
Read Chapter 11
Homework 6 (Due on Tuesday, February 24)
1) Ex. 11.3a, also for the positive +1 ions, and use the g or u orbital notation; 2) Ex. 11.2a using bonding and antibonding notation, and also give their bond orders; 3) Ex. 11.7a, and also give their normalization constant in terms of the overlap integral; 4) Ex. 11.8a; 5) Using the expressions given in class for the sp^2 hybrids, show that they are orthogonal and normalized; 6) Ex. 11.11a; 7) Ex. 11.12b but for the doubly charged (+2) ions; 8) Ex. 11.13a, only part (a).
Read Chapter 12 as covered in class
Homework 7 (Due on Tuesday, March 3)
1) Ex. 12.9a; 2) Ex. 12.2a ; 3) Ex. 12.6a; 4) Ex. 12.12a; 5) Work out the details of self-test 12.7; 6) Ex. 12.13a
Read Chapter 13, sections 13.1 to 13.13.
Homework 8 (Due on Tuesday, March 24)
1) Ex. 13.1a but for (b) 400 nm and (c) 2,500 cm^{-1}; 2) Ex. 13.5a but for the 3 ß2 transition; 3) Ex. 13.8a; 4) Ex. 13.11a; 5) Ex. 13.16a; 6) Ex. 13.12a; 7) Ex. 13.22a.
Read Chapter 13, and sections 14.1 and 14.2.
Homework 9 (Due on Tuesday, March 31)
1) Ex. 13.20a; 2) Ex. 13.21a; 3) Ex. 13.24a; 4) Ex. 13.4a but for a rate of 5.0X10^{12} coll/s; 5) Probl. 13.2, only (b); 6) Probl. 13.4; 7) Ex. 14.2a, but for a solution of thickness 3.0 mm; 8) Probl. 14.6; 9) Probl. 14.16.
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Read Chapter 14, and subsection 11.4(e).
Homework 10 (Due on Tuesday, April 7)
1) Ex. 14.11a, and also guess which transition for ionization of D_2 is the largest; 2) Probl. 14.8; 3) Probl. 14.10, but for a ratio of 2.0X10^{5}; 4) Give details of the solution to self-test 14.3; 5) Ex. 11.10a, also when the ion ends with a vibrational energy of 0.10 eV.
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Read Chapter 15.
Homework 11 (Due on Tuesday, April 14)
1) Ex. 15.2a, and also give how many spectral lines appear for a single nucleus; 2) Ex. 15.7a, only (a) and (c); 3) Ex. 15.9a and Ex. 15.10a; 4) Ex. 15.16a; 5) Ex. 15.18a. Optional: solve Ex. 15.15a for an extra five points.
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Read Chapter 16, and sections 17.1, 17.2, and 17.8 of Chapter 17.
Homework 12 (Due on Tuesday, April 21)
1) Ex. 16.4a, and also calculate the probability for each energy level; 2) Ex. 16.2a and also calculate the thermal deBroglie wavelengths each energy level; 3) Ex. 16.8a only for (b) to (e); 4) Ex. 16.12a; 5) Ex. 17.10a. Optional problem for an extra five points: Ex. 17.14a.
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Progress Tests
Test 1: Tuesday, February 10, given in class . Covering lectures up to and including the lecture on February 3, and homeworks 1 to 4, plus HW 5 as it relates to atoms. Answers for test 1
Test 2: Thursday, March 5, given in class. Covering lectures from Feb. 5 up to and including the lecture of Feb. 26 (Chapters 11 and 12 of the combined volume, as covered in class), and homeworks 5, 6, and 7, as they relate to molecules. Answers for test 2.
Test 3: Tuesday, April 21, in class. Covering lectures starting on March 17 and ending on April 16 (Chapters 13 to 16 of the combined volume, as covered in class) and homeworks 8 to 12 .
Students may use their own personal lecture notes during a test, but not the textbook or its copies, nor an e-book. Calculators are allowed, but cell phones and PDAs are not allowed during the tests.
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