Material taught, literature references, homework

4/10/2024: What is and what is not discussed as Spectroscopy. Quantities involved. Appearance of a spectum. Basic equations and spectral regions. Blackbody radiation, Einstein coefficients.

Hollas: xxi-xxv, 27-39, 41-43
Bernath (2nd Ed.): 3-11
McHale: 48-51
Softley: 1-6
Brown: 1-5, 15-17

11/10/2024: Einstein coefficients. Line shapes, broadening effects: Natural, Doppler, pressure, etc.

Hollas: 27-39, 1-8
Bernath: 7-11, 21-34
McHale: 48-51, 153-170
Softley (en): 17-18
Brown (en): 14-17

Homework

Problem 1: The double D line of sodium has an average wavelength of 589.29 nm. Write the frequency, the wavenumber, the energy (in J and eV) of its photon. In which spectral region does it belong?

18/10/2024: Atomic spectroscopy: Hydrogen-like atoms, wave functions, spin-orbit coupling, fine structure, hyperfine structure, quantum defect theory for spectra of alkali metals

Hollas: 34-39, 1-12
Bernath: 109-124, 137-141
Softley: 8-25, 29-35
Sobelman: 3-15, 34-37, 156-162

Homework

Problem 2: At what wavenumber dows a black body with a temperature of 37 °C emit its most intense radiation? What part of the electromagnetic spectrum does it fall under?

Problem 3: How many electrons does ¹⁰⁸Ag⁴⁶⁺ possess?

Problem 4: At what wavenumber and wavelength is the 4th Balmer line observed?

25/10/2024: Atomic spectroscopy: wave functions, Einstein coefficients and transition dipole moments. Demonstration of UV-vis. spectrophotometer operation and components. Range of visible spectrum. Flame spectroscopy with a Bunsen burner.

Spectra of H, O, He, Ne, Ar, Na, Li, sun

4/11/2024: Rotational spectroscopy: enery levels, angular momentum, moments of inertia of molecules, calculating moments of inertia, types of tops. Diatomic and linear molecules: hamiltonian operator, quantum numbers, energy eigenvalues, wave functions, degeneracy, selection rules, population distributions, peak positions, form of spectra, isotope effect.

Brown: 21-26
Hollas: 103-111
Bernath: 169-177
McHale: 209-212
Carrington: 146-152
Levine: 165-168

Homework

Problem 5: Using data from CRC Handbook of Chemistry and Physics (9- 15-41) caclulate the moments of inertia for the moelcules HBr, C₂H₂, HCCD and their rotational spectroscopic constants (in cm^-1). Use the masses of the most abundant isotopes when not specified.

8/11/2024: Rotational spectroscopy of non-linear molecules: Hamiltonian operator, quantum numbers, energy and angular momentum eigenvalues, wavefunctions, degeneracy, selection rules, centrifugal distortion, form of spectra.

Brown: 26-29
Bernath: 174-176, 185-200
Zare: 85-86, 89
Hollas: 103-105, 113-114
Banwell: 31-50
Levine: 195-213

Geometry data and rotational constants of molecules

Homework

Problem 6: Pure rotational transitions of ¹²C³²S in the ground vibrational state are observed in the microwaves at the frequencies 48990.978 MHz (J=0→1), 97980.950 MHz (J=1→2), 146969.033 MHz (J=2→3), 195954.226 MHz (J=3→4). Determine the the spectroscopic constants based on the transitions ovserved. Caclulate the bond length at the ground vibraional state.

22/11/2024: Vibrational spectroscopy of diatomic molecules: Potential energy curve, harmonic oscillator, Morse potential, energy, quantum numbers, energy levels, vibrational population distribution, zero point energy, spectroscopic constants, wave functions, selection rules, Dunham coefficients.

Bernath: 208-221
Hollas: 137-147
Banwell: 55-63
McHale: 248-257, 266-267
Brown: 32-42

Homework

Problem 7: Calculate the force constant (in N/m) for H₂ (ω_e = 4320 cm^-1) and Na₂ (ω_e = 0.221 cm^-1).

Problem 8: Write down the expression for the vibrational transitions with Δv = 1 of a diatomic molecule described by the spectroscopic constants ω_e, ω_ex_e, ω_ey_e, Calculate the transition wavenumber for v" = 5 of NaBr for which these constants have the following values 315 cm^-1, 1.15 cm^-1 and 0.0008 cm^-1.

29/11/2024: Vibrational spectroscopy of diatomic molecules: vibrational and rotational, coupling constants of vabrational and rotational motion, vibrational-rotational transitions, R and P branches, spectral patterns, mass dependence of Dunham coefficients on isotope substitution

Bernath: 223
Hollas: 147-151
Levine: 142-174
Banwell: 63-71
Brown: 42-49

Homework

Problem 9: Write down the expression for the vibrational and rotational transitions belonging to the P branch of the first overtone transition of a diatomic molecule described by the spectroscopic constants ω_e, ω_ex_e, ω_ey_e, B_e, α_e.

6/12/2024: Vibrational spectroscopy for polyatomic molecules: degrees of freedom, normal modes, local modes, types of vibrations (streching, bending, etc.), degeneracy, vibrational angular momentum, types of potentials, rotational structure. Demonstration of normal modes on the computer using GausView. Fourier transform, interferometer and mathematical expressions.

Bernath: 226-230, 248, 250, 256-259, 262-264, 268, 270-271, 280
Hollas: 154-162, 166-168, 174-195
Banwell: 71-83
McHale: 270-305
Levine: 235-245, 258-260

Homework

Problem 10: Make a rough drawing of the potential energy curve for the internal rotation of 1,2-dichloroethane and 2-fluoro-ethenol.

Problem 11: H₂O spectroscopic constants for its ground electronic state (ν_i is used in place of ω_e): ν₁ = 3825.32 cm^-1, ν₂ = 1653.91 cm^-1, ν₃ = 3935.59 cm^-1, x₁₁ = -43.89 cm^-1, x₂₂ = -19.5 cm^-1, x₃₃ = -46.37 cm^-1, x₁₂ = -20.02 cm^-1, x₁₃ = -155.06 cm^-1, x₂₃ = -19.81 cm^-1. Calculate the wavenumber for the following vibrational transitions: (v₁" v₂" v₃") → (v₁' v₂' v₃') = (000) → (001), (000) → (201), (000) → (004).

12/12/2024: Vibrational spectroscopy of polyatomic molecules: overtone and combination transitions. Electronic spectroscopy of diatomic molecules: Potential energy curves, quantum numbers, nomencleture, spectroscopic terms, selection rules. Shapes of spectra, positions and shapes of potential energy curves, line position calculation, Fortrat diagrams, Hund's cases of angular momentum coupling, sequences and progressions.

Bernath: 24, 321-326
Hollas: 48-59, 225-237
Banwell: 20-26, 93-96, 162-163, 182-186
Brown: 57-60, 64-74

Homework

Problem 12: Indicate which of the following transitions are allowed and which are forbidden. i) ²Π_3/2 - ²Φ_5/2, ii) ²Π_3/2 - ¹Σ⁺, iii) ¹Π_u - ³Π_g, iv) ²Π_3/2 - ²Σ^-, v) ¹Σ^-_g - ¹Σ^-_g, vi) ¹Π_3/2 - ¹Π_3/2