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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 Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
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
De Broglie proposed that the frequency f of a matter wave equals E/h, where E is the total energy of the particle and h is the Planck constant.For a particle at rest, the relativistic equation E=mc 2 allows the derivation of the Compton frequency f for a stationary massive particle, equal to mc 2 /h.
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).
The 41.8% point is the wavelength-frequency-neutral peak (i.e. the peak in power per unit change in logarithm of wavelength or frequency). These are the points at which the respective Planck-law functions 1 / λ 5 , ν 3 and ν 2 / λ 2 , respectively, divided by exp ( hν / k B T ) − 1 attain their maxima.
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.
Bond energy and bond-dissociation energy are measures of the binding energy between the atoms in a chemical bond. It is the energy required to disassemble a molecule into its constituent atoms. This energy appears as chemical energy , such as that released in chemical explosions , the burning of chemical fuel and biological processes.