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Boltzmann constant: The Boltzmann constant, k, is one of seven fixed constants defining the International System of Units, the SI, with k = 1.380 649 x 10 −23 J K −1. The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule).
In the physical sciences, the wavenumber (or wave number), also known as repetency, [1] is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m-1).
For example, the atomic mass constant is exactly known when expressed using the dalton (its value is exactly 1 Da), but the kilogram is not exactly known when using these units, the opposite of when expressing the same quantities using the kilogram.
Here, k ≈ 1.38 × 10 −23 J/K is the Boltzmann constant and kT 0 is the available noise power density (the noise is thermal noise, Johnson noise). As a numerical example: A receiver has a bandwidth of 100 MHz, a noise figure of 1.5 dB and the physical temperature of the system is 290 K.
The vibrational temperature is commonly used in thermodynamics, to simplify certain equations.It has units of temperature and is defined as = ~ = where is the Boltzmann constant, is the speed of light, ~ is the wavenumber, and (Greek letter nu) is the characteristic frequency of the oscillator.
For a system (such as a molecule or solid) with uncoupled vibrational modes the vibrational partition function is defined by =, where is the absolute temperature of the system, is the Boltzmann constant, and , is the energy of the jth mode when it has vibrational quantum number =,,, ….
It gives the most recent values published, and will be updated when newer values become available, which is typically every four years. The values have been updated to the CODATA 2022 values. This includes the 2019 revision of the SI , which made the values of several constants exact (e.g. e ), whereas some previously exactly defined constants ...
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.