Molecular Spectroscopy and Structure Review

A comprehensive set of vocabulary flashcards covering the basic principles of molecular spectroscopy, energy quantization, line broadening, and laser operation based on the lecture notes.

Spectroscopy

The measurement and interpretation of absorption and emission of electromagnetic radiation when atoms, molecules, or ions move from one energy level to another.

Electromagnetic Radiations

Radiations possessing oscillating electric and magnetic fields in planes perpendicular to the direction of propagation, traveling with the velocity of light $c$.

Planck's Constant ($h$)

A fundamental constant used to calculate energy associated with a wave ($E = hv$), equal to $6.626 \times 10^{-34}\,Js$.

Wavenumber ($\bar{v}$)

The reciprocal of wavelength ($\bar{v} = 1/\lambda$), commonly expressed in units of $cm^{-1}$ or $m^{-1}$.

Translational energy ($E_t$)

Energy due to the translational motion of a molecule; it is not quantized for a fluid in a container because the available space is large compared to molecular dimensions.

Electronic energy ($E_e$)

Energy arising from the continuous motion of electrons associated with each atom or bond.

Vibrational energy ($E_{\upsilon}$)

Energy due to the periodic displacement of atoms from their equilibrium position, involving restoring forces of the bonds.

Rotational energy ($E_r$)

Energy a molecule possesses by virtue of bodily rotation about its center of gravity.

Born and Oppenheimer Approximation

The assumption that the various forms of molecular energies (electronic, vibrational, and rotational) are independent of each other, where $E_{total} = E_e + E_{\upsilon} + E_r$.

Electronic Spectra

Spectra produced by transitions between electronic energy levels, typically occurring in the visible or ultraviolet regions.

Vibrational Spectra

Spectra resulting from transitions between vibrational levels within the same electronic level, falling in the infrared region.

Rotational Spectra

Spectra resulting from transitions between rotational levels within the same vibrational level, falling in the far infrared or microwave region.

Fluorescence

A process where a system is excited to an upper state by absorption and decays back to a lower state in a time less than $10^{-5}\,s$; the emission is typically lower in frequency than the absorbed radiation ($\nu < \nu_0$).

Phosphorescence

A phenomenon where a molecule loses energy via a non-radiative transition to a metastable state, resulting in a delayed re-emission of radiation that continues after the exciting source is removed.

Rayleigh Scattering

Elastic scattering where the scattered radiation has the same frequency as the incident radiation ($\nu = \nu_0$).

Raman Effect

Inelastic scattering where photons undergo energy exchange with molecules, resulting in frequency shifts characteristic of vibrational or rotational energies ($\nu = \nu_0 \pm \nu_m$).

Stokes Lines

Raman spectral lines that appear on the low-frequency side of the Rayleigh line ($\nu = \nu_0 - \nu_m$) when a molecule gains energy from a photon.

Anti-Stokes Lines

Raman spectral lines that appear on the high-frequency side of the Rayleigh line ($\nu = \nu_0 + \nu_m$) when a molecule loses energy to a photon.

Natural Line Width

Broadening arising because energy levels are not precisely determined, governed by the uncertainty relation $\Delta E \cdot \Delta t = \frac{h}{2\pi}$.

Collision (Pressure) Broadening

The broadening of energy levels and spectral lines caused by the perturbation of molecular energies during collisions.

Doppler Broadening

Broadening caused by the Doppler shift in absorption and emission frequencies due to the random motion of atoms or molecules, resulting in a Gaussian line shape.

Saturation (Power Broadening)

A phenomenon occurring when the rate of absorption approaches zero because the populations of the two energy states approach equality ($N_n / N_m \approx 1$).

Spontaneous Emission

The process of a molecule in an excited state emitting a photon without the influence of an external agency; the resulting light is incoherent.

Stimulated Emission

The process where an upper-state molecule is stimulated to release a quantum of energy by the presence of another quantum of equivalent energy; the output light is completely coherent.

Einstein's A Coefficient ($A_{21}$)

The probability per unit time for spontaneous emission.

Einstein's B Coefficient ($B_{12}$ or $B_{21}$)

The probability per unit time for induced absorption or stimulated emission.

LASER

An acronym for Light Amplification by Stimulated Emission of Radiation, based on generating population inversion to amplify incident radiation.

Population Inversion

A non-equilibrium situation where the number of atoms in an excited state ($n_2$) is greater than the number in the lower state ($n_1$).

Coherence

A characteristic of laser radiation where waves bear the same phase relationship to each other at all times; it can be spatial or temporal.

Reduced Mass ($\mu$)

Effective mass used in the study of diatomic molecules, defined as $\mu = \frac{m_1 m_2}{m_1 + m_2}$.

Zero-point Energy

The lowest vibrational energy level ($\upsilon = 0$) of a harmonic oscillator, equal to $\frac{1}{2}h\nu_0$, in accordance with the uncertainty principle.

Selection Rule

Conditions that summarize whether a radiative transition between quantum states is possible; for a rigid diatomic rotor, it is $\Delta J = \pm 1$, and for a harmonic oscillator, it is $\Delta \upsilon = \pm 1$.

Polarizability ($\alpha$)

The constant of proportionality between an induced dipole moment $P$ and an applied electric field $E$ ($P = \alpha E$); its change is necessary for Raman activity.