3: Homework Solutions

Sacramento City College
CHEM 309: General, Organic and Biochemistry
Prof. Dianne Bennett

Agenda (Fall)  •   Agenda (Spring)  •  Homework Problems

1. Chapter 2: The Classical Wave Equation
2. 2.1: The One-Dimensional Wave Equation
3. 2.2: The Method of Separation of Variables
4. 2.3: Oscillatory Solutions to Differential Equations
5. 2.4: The General Solution is a Superposition of Normal Modes
6. 2.5: A Vibrating Membrane
7. 2.E: The Classical Wave Equation (Exercises)

 •  Homework Solutions

1. Chapter 11: Computational Quantum Chemistry
2. 11.1: Gaussian Basis Sets
3. 11.2: Extended Basis Sets
4. 11.3: Orbital Polarization Terms in Basis Sets
5. 11.4: The Ground-State Energy of H2H2
6. 11.5: Quantum Calculations
7. 11.E: Computational Quantum Chemistry (Exercises)

Chapters

1. Chapter 12: Group Theory: The Exploitation of Symmetry
2. 12.1: The Exploitation of Symmetry
3. 12.2: Symmetry Elements
4. 12.3: Symmetry Operations Define Groups
5. 12.4: Symmetry Operations as Matrices
6. 12.5: The C3VC3V Point Group
7. 12.6: Character Tables
8. 12.7: Characters of Irreducible Representations
9. 12.8: Using Symmetry to Solve Secular Determinants
10. 12.9: Generating Operators
11. 12.E: Group Theory: The Exploitation of Symmetry (Exercises)

  •  Video Tutorials

1. Chapter 13: Molecular Spectroscopy
2. 13.1: The Electromagnetic Spectrum
3. 13.2: Rotations Accompany Vibrational Transitions
4. 13.3: Unequal Spacings in Vibration-Rotation Spectra
5. 13.4: Unequal Spacings in Pure Rotational Spectra
6. 13.5: Vibrational Overtones
7. 13.6: Electronic Spectra Contain Electronic, Vibrational, and Rotational Information
8. 13.7: The Franck-Condon Principle
9. 13.8: Rotational Spectra of Polyatomic Molecules
10. 13.9: Normal Modes in Polyatomic Molecules
11. 13.10: Irreducible Representation of Point Groups
12. 13.11: Time-Dependent Perturbation Theory
13. 13.12: The Selection Rule for the Rigid Rotator
14. 13.13: The Harmonic Oscillator Selection Rule
15. 13.14: Group Theory Determines Infrared Activity
16. 13.E: Molecular Spectroscopy (Exercises)

 •  Basic Knowledge Practice Quizzes

Radioisotopes

(01) In chemical reactions, the valence electrons change. In nuclear reactions, the protons and neutrons change within the nuclei of the atoms.

(02) Atoms with the same Z (atomic number) and different A (mass number)

(03) Demonstrate your understanding of isotopes by filling in the blank portions of the table below.

Isotope Name	Atomic Number	Mass Number	Number of Neutrons	Number of Protons
Carbon-14	6	14	8	6
Polonium-211	84	211	127	84
Potassium-40	19	40	21	19
Plutonium-244	94	244	150	94
Iodine-130	53	130	77	53
zinc-66	30	66	36	30

Electromagnetic Radiation

(04) X-rays excite core electrons. Gamma-rays can cause the loss of core electrons creating ions and radicals.

(05) radio < microwave < infrared < visible < ultraviolet < X-ray < gamma-ray

(06)

1. microwaves
2. X-rays
3. visible light

(07) UV light can be harmful because the higher energy light can penetrate our skin to cause sunburns and other biological damage.

(8) The following may or may not be forms of electromagnetic radiation. Identify which ones are, and if they are, determine whether they are more benign or harmful.

Gamma rays; Microwaves; X-Rays

Types of Radioactive Decay

(09) Alpha daughter is \(\ce{^{228}_{88}Ra}\). the beta daughter is \(\ce{^{232}_{91}Pa}\).

(10) \(\ce{^{240m}U \rightarrow ^{240}U + \gamma} \)

(11) Alpha decay releases a helium nucleus. The conversion of a neutron to a proton releases an electron in beta decay. The conversion of a proton to a neutron releases a positron in positron decay. Gamma decay releases high energy electromagnetic radiation in the gamma ray region.

(12) For each isotope, according to the listed type of decay, name the daughter nuclide produced.

1. beryllium-10
2. aluminum-28
3. neon-18
4. cobalt-56
5. rhenium-189

(13)

1. \(\ce{^{73}_{32}Ge \rightarrow ^{69}_{30}Zn} + \alpha\)
2. \(\ce{^{89}_{39}Y \rightarrow ^{89}_{38}Sr} + \beta^+\)
3. \(\ce{^{40}_{19}K \rightarrow ^{40}_{20}Ca} + \beta^-\)
4. \(\ce{^{137m}_{56}Ba \rightarrow ^{137}_{56}Ba + \gamma}\)

Half-Life

(14) 4 half-lives; 1 g left; 6.25% remaining

(15) 5 half-lives; 3.125 g remaining

(16) 3 half-lives; 103.5 hours; 12.5% of original sample remains

(17) Shorter half-life to minimize exposure and reduce disruption in daily ife.

(18) 4 g remain after 4 half-lives. Sometime between the 4th and 5th half-lives, the sample will fall below the 5% guideline.

(19) 2 half-lives or 88 days

Artificial Radioisotopes

(20) \(\ce{^{252}_{99}Es + 3 ^1_0n \rightarrow ^{255}_{102}No} + 3 \beta^-\)

(21) \(\ce{^{12}_6C + 2 ^1_0n \rightarrow ^{14}_{6}C}\)

(22) \(\ce{^{22}_{12}Mg^{2+}}\)

Energy and Penetrating Power of Nuclear Radiation

(23) The lead absorbs the X-rays.

(24) relative energy: X-rays < gamma-rays < beta/positrons < alphas

penetrating power: alpha < beta/positron ≈ X-ray < gamma

(25) Betas and positrons because they have similar mass and energy with opposite charge.

Measurement of Radiation

(26)

1. chronic
2. acute
3. chronic
4. chronic
5. acute