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A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
A hydrogen atom with proton and electron spins aligned (top) undergoes a flip of the electron spin, resulting in emission of a photon with a 21 cm wavelength (bottom) The hydrogen line, 21 centimeter line, or H I line [a] is a spectral line that is created by a change in the energy state of solitary, electrically neutral hydrogen atoms.
Symmetric transversal vibrations with frequency ω s 2 = 2 k 2 M m A m B {\displaystyle \omega _{s2}={\sqrt {\frac {2k_{2}M}{m_{A}m_{B}}}}} In the previous formulas, M is the total mass of the molecule, m A and m B are the masses of the elements A and B, k 1 and k 2 are the spring constants of the molecule along its axis and perpendicular to it.
The asymmetric stretching vibration, of B 2 symmetry in the point group C 2v is a normal vibration. The H-O-H bending mode origin is at 1595 cm −1 (ν 2 , 6.269 μm). Both symmetric stretching and bending vibrations have A 1 symmetry, but the frequency difference between them is so large that mixing is effectively zero.
Electronic and vibrational levels of the hydrogen molecule. In reference to the figure shown, Lyman-Werner photons are emitted as described below: A hydrogen molecule can absorb a far-ultraviolet photon (11.2 eV < energy of the photon < 13.6 eV) and make a transition from the ground electronic state X to excited state B (Lyman) or C (Werner).
For most reactions of interest, a hydrogen atom is transferred between two atoms, with a transition-state [A···H···B] ‡ and vibrational modes at the transition state need to be accounted for. Nevertheless, it is still generally true that cleavage of a bond with a higher vibrational frequency will give a larger isotope effect.
Isotopic shifts are best known and most widely used in vibration spectroscopy, where the shifts are large, being proportional to the ratio of the square root of the isotopic masses. In the case of hydrogen, the "H-D shift" is (1/2) 1/2 ≈ 1/1.41. Thus, the (totally symmetric) C−H and C−D vibrations for CH 4 and CD
The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule.It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking, such as the existence of unbound states.