Spectroscopy and Quantum Mechanics Quiz

Waves

• Waves are oscillations propagating through a medium, often electromagnetic or mechanical.
• Diffraction occurs when waves encounter obstacles or slits, causing bending and spreading.
• Spectroscopy analyzes matter by its interaction with waves, determining properties like composition, structure, and energy levels.

Schrödinger Equation in a Potential Well

• The Schrödinger equation describes the quantum behavior of particles in a potential well.
• A potential well confines a particle, leading to discrete energy levels.
• Wavefunction solutions in a finite or infinite potential well indicate quantized states, restricting the particle's energies.

Diffraction and Spectroscopy

• Spectroscopy studies how matter interacts with electromagnetic waves to analyze its composition, structure, and energy states.
• Diffraction is the bending and spreading of waves when they encounter an obstacle or pass through a narrow slit, creating interference patterns.

Calculating Absorption Coefficients

• Absorption coefficients quantify how much light a material absorbs over a specific distance.
• Calculated using the Beer-Lambert Law, which uses the absorbance (A), path length (d), and absorption coefficient (α).
• Equation: α = 2.303 * (absorbance/path length)

Transition Probability

• Transition probability between energy levels can be calculated using Fermi's Golden Rule.
• Equation: P_if= 2π|⟨f|H′|i⟩|² ρ(E_f) / h
• Where P_if is the transition probability, H′ is the perturbation, ⟨f|H′|i⟩ is the matrix element of the interaction, and ρ(E_f) is the density of final states at energy E_f.

Factors Affecting Peak Heights in Absorption

• Absorption coefficients are influenced by transition dipole moments, the density of states, transition probability, concentration of absorbing species, and linewidth (broadening).
• Equation: (α(ω)) ∝ N/hω * ρ(E), where N is number of absorbers, hω is the incident energy, ρ(E) is density of states

Spectroscopy for Single Crystals

• Absorption spectroscopy can be performed on single crystals, but orientation matters for light interaction with crystal planes.
• Absorption properties depend on crystal symmetry and incident light's polarization.

Periodicity in a Diffraction Pattern

• Periodicity (P) in a diffraction pattern is the distance between maxima.
• Equation: P=(distance between points on the wall) / (distance from person to wall) or P = X (distance between points in diffraction pattern)

Phase and Spectroscopy

• Phase of light interacts with matter in spectroscopy, affecting coherence and interference patterns.
• Phase transitions in materials (e.g. solid, liquid, gas) affect Raman vibrational modes, leading to shifts in peak positions and intensities.

Raman Spectroscopy

• Raman spectroscopy analyzes the phase-related interactions of light with molecular vibrations, offering insights into molecular structure and dynamics.
• Raman scattering involves inelastic scattering of light, revealing shifts in energy and phase.

Laser Emission and Raman Spectroscopy

• Laser emission occurs due to stimulated emission of coherent photons, often highly focused and monochromatic.
• Narrow linewidth lasers are crucial for Raman spectroscopy, allowing detailed analysis of vibrational modes with high spectral resolution.