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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.
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.
The strength of a bond can be estimated by comparing the atomic radii of the atoms that form the bond to the length of bond itself. For example, the atomic radius of boron is estimated at 85 pm, [10] while the length of the B–B bond in B 2 Cl 4 is 175 pm. [11] Dividing the length of this bond by the sum of each boron atom's radius gives a ratio of
The term bond-dissociation energy is similar to the related notion of bond-dissociation enthalpy (or bond enthalpy), which is sometimes used interchangeably.However, some authors make the distinction that the bond-dissociation energy (D 0) refers to the enthalpy change at 0 K, while the term bond-dissociation enthalpy is used for the enthalpy change at 298 K (unambiguously denoted DH° 298).
When the frequency of the IR matches the vibrational frequency of a bond or collection of bonds, absorption occurs. Examination of the transmitted light reveals how much energy was absorbed at each frequency (or wavelength). This measurement can be achieved by scanning the wavelength range using a monochromator.
[notes 3] A bond length obtained in this way is slightly different from the equilibrium bond length. This is because there is zero-point energy in the vibrational ground state, to which the rotational states refer, whereas the equilibrium bond length is at the minimum in the potential energy curve. The relation between the rotational constants ...
The Faraday effect is chromatic (i.e. it depends on wavelength), and therefore the Verdet constant is quite a strong function of wavelength. [ 5 ] [ 6 ] At 632.8 nm , the Verdet constant for TGG is reported to be −134 rad /( T ·m) , whereas at 1064 nm it falls to −40 rad/(T·m) . [ 7 ]
For example, a wavenumber in inverse centimeters can be converted to a frequency expressed in the unit gigahertz by multiplying by 29.979 2458 cm/ns (the speed of light, in centimeters per nanosecond); [5] conversely, an electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space.