Inverse centimeters

Fourier-transform infrared (FTIR) spectroscopy Spectroscopy based on excitation of vibrational modes of chemical bonds in a molecule. The energy of the infrared radiation absorbed is expressed in inverse centimeters (cm ), which represents a frequency unit. For transition-metal complexes, the ligands -C N and -C=0 have characteristic absorption bands at unusually high frequencies, so that they are easily distinguished from other bonds. The position of these bonds depends on the distribution of electron density between the metal and the ligand an increase of charge density at the metal results in a shift of the bands to lower frequencies. 

Fig. 3. Numerical calculated position and intensities of the pure rotational spectrum of dipolarly unstable tetrahedral systems for the following parameter values (in inverse centimeters) A = 0.5, B = 5.24, kT = 200. Marked with crosses and circles and unmarked are the R, R", and R branches, respectively, with the Q transition indicated by an arrow (p is the gas pressure in amagat units).

Here K is expressed in units of inverse centimeters and the magnetic fields are expressed in Tesla. The pendulum equation can be rednced to... 

For convenience, chemists generally report infrared frequencies as wavenumbers. For a given vibrational frequency (y) the wave-number (y) is given hy v = vjc, where c is the speed of light in cm s . Because frequencies are in units of s (or Hz), the wave-number corresponding to that frequency will have units of cm (or inverse centimeters). To see the usefulness of this transformation, consider the vibrational frequency of CO, which is 6.503 X 10 s when reported in Hz, but only 2170 cm when reported in wave-numbers. 

We also need to be aware of the macroscopic cross section that is used to determine reaction rates. The macroscopic cross section applies to a material as a whole and has units of inverse centimeters (usually interpreted as the probability of interaction per cm of travel of a free neutron). This cross section is problem-dependent, is usually denoted by the upper case Greek sigma, and is related to the microscopic cross section through the relationship ... 

The units of wavenumber are inverse centimeters (cm ), and the values range from 400 to 4000 AH of the spectra in this chapter will be reported in wavenumber rather than wavelength. 

Another important property of a light wave is its wavenumber, which is denoted by the letter W. The wavenumber measures the number of cycles a wave undergoes per unit length. Wavenumbers are measured in units of cycles per centimeter, which are frequently abbreviated as cm- and can be pronounced as inverse centimeters, reciprocal centimeters, or wavenumber. If a spectrum has a peak at 3000 cm it means the sample absorbed infrared light that underwent 3000 cycles per centimeter. Most infrared spectra are plotted from 4000 to 400 cm on the x-axis, as seen in Figure 1.2. 

By convention, IR spectra are printed upside-down, so the peaks look like valleys. Another thing to look out for is that the x axis is marked in wavenumbers, also ealled inverse centimeters (cm ), instead of frequency (Hz). Since cm are proportional to Hz, cm are just another unit for frequency. 

Another problem is that the units are confusing. Wavenumbers or inverse centimeters (cm ) are simply measures of frequency. Higher wavenumber higher frequency. 

Depth of EB penetration The depth of penetration of energetic electrons into a material at normal angle of incidence is directly proportional to the energy of the electrons and inversely proportional to the density of the material [49,50]. The depth is expressed as a product of penetration distance and the density of the material (i.e., 1 g/cm = 1 cm X 1 g/cm ). The radiation energy and thus the type of electron accelerator to be used are dependent on the required penetration depth, the density of the irradiated material, and the chosen irradiation system. If one measures the density (d) in gram per cubic centimeter (g/cm ) and the layer thickness (T) in millimeter (mm), one can determine the radiation energy ( ) necessary for optimal homogeneity from [40] ... 

Viscosity is then a measure of the resistance of a material to flow. In fact, the inverse of viscosity is given the name fluidicity. A material s resistance to flow increases with its viscosity. Viscosity has been reported using a number of different names. The centimeter-gram-second (CGS) unit of viscosity is called the poise, which is a dyne seconds per square centimeter. Another widely used unit is the pascal (or Pa), which is Newton seconds per square centimeter. In fact, 1 Pa= 10 poise. 

As noted earlier, the inverse of p is called conductivity and is generally given in siemens per centimeter (S/cm) (S= 1/ohm). The SI unit of conductivity is S/m, but it is often reported as S/cm so attention should be paid as to which unit is being used. A graph of conductivity for many materials is given in Section 19.1. 

Absolute dosimetry with the electron accelerator is less accurate than with the cobalt-60 source since penetration of the electron is a variable— directly proportional to the energy of the beam and inversely proportional to the density of the material. The absorbed dose varies with depth (18) and is about 60% of maximum at the surface with a steady increase to a maximum at about one-third of the total penetration depth. At about two-thirds of the total penetration, the dose is equivalent to that absorbed at the surface. Therefore, if all parts of the sample are to receive the same minimum dose, the useful penetration is approximately two-thirds of the total, or about 0.33 gram per square centimeter per m.e.v. 

Propagation Delay of Lossless Lines. The minimum propagation delay (Tpd expressed in picoseconds per centimeter) for a unit length of lossless line is the inverse of the phase velocity (op) of the electromagnetic waves propagating through the dielectric medium surrounding the conductor line ... 

The diffusion flux J, in moles per square centimeter, is proportional to the concentration gradient and inversely proportional to the diffusion layer s effective thickness SN (also called Nernst thickness). The proportionality constant D is the diffusion constant hence... 

For membranes of equal pore area and porosity (e), the number of square centimeter is proportional to the inverse square of the pore That is,... 

Conductance is measured in a cell between two chemically inert electrodes it is directly proportional to the electrode surface area and inversely proportional to the distance between them. Conductivity is usually expressed in microohms per centimeter (pmho/cm). In the International System of Units, the reciprocal of ohm is siemens (S), and in this system conductivity is expressed as millisiemens per meter (mS/m) or microsiemens per centimeter (pS/cm). Ten pmhos/cm are equal to one mS/m. 

FIG. 18. Reaction parameters for n-hexane conversion by Ni and Ni-Cu alloys at 330°C Ai = log rw (rate per gram of catalyst) A2 = log rs (rate per square centimeter of total surface) Eact is activation energy of the overall process S is the selectivity for producing Cg products M is a fission parameter whose value inversely reflects the degree of multiple fragmentation to methane (102). 

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