8: Electronic Spectroscopy
- Page ID
- 521445
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 8.2: Electronic Spectra Contain Electronic, Vibrational, and Rotational Information
- This page discusses how molecules undergo electronic transitions during microwave and infrared absorptions, linked to vibrational and rotational states. It explains that energy levels come from electronic potential energy curves and that electronic transitions simplify calculations by being independent of rotational effects.
- 8.3: The Franck-Condon Principle
- This page explains the Franck-Condon Principle, detailing how electronic transitions in spectroscopy occur with minimal nuclear change. It highlights the significance of the Franck-Condon overlap integral, connecting transition probabilities to vibrational wavefunction overlaps.
- 8.4: Term Symbols Gives a Detailed Description of an Electron Configuration
- This page explains the relationship between electron configurations and angular momentum, focusing on quantum numbers such as total orbital angular momentum (L), total magnetic quantum number (M_l), total spin magnetic quantum number (M_s), and total intrinsic spin quantum number (S).
- 8.5: The Allowed Values of J - the Total Angular Momentum Quantum Number
- This page discusses L-S coupling in multi-electron atoms, particularly for lighter elements, where orbital and spin angular momenta combine to define total angular momentum and corresponding term symbols formatted as \(^{2S+1}L_J\). It illustrates this with the hydrogen atom's ground state term symbol \(^2S_{1/2}\), reflecting its spin states and angular momentum. Additionally, the text provides exercises on writing term symbols for various quantum numbers.
- 8.6: Hund's Rules Determine the Term Symbols of the Ground Electronic States
- This page explains Hund's three rules for electron configurations in multi-electron systems. It emphasizes maximizing spin multiplicity, orbital angular momentum, and stability based on orbital fill levels. The first rule states electrons occupy empty orbitals to reduce repulsion. The second maximizes total angular momentum, and the third differentiates between less than and greater than half-filled configurations.
- 8.7: Using Atomic Term Symbols to Interpret Atomic Spectra
- This page explores spin-orbit coupling in atomic spectroscopy, detailing its role in fine structure, which explains closely spaced spectral lines in hydrogen and sodium atoms. It discusses selection rules for electronic transitions, particularly in heavier atoms, and provides specific examples, such as the sodium D-line (589.0 nm and 589.6 nm) and the hydrogen \(H_{\alpha}\) line (656.279 nm), both influenced by spin-orbit interactions.