Short wavelength limit

Fig. 1-3. The continuous x-ray spectrum. Note that the short-wavelength limit (Eq. 1-2) is 0.248 A for 50 kv and 0.620 A for 20 kv. A spectrum from a rectified a-c tube would have the peak displaced to the right and for a given input energy would have less x-ray output. (After Ulrey, Phys. Rev. [2], 11, 401.)...

All spectra begin abruptly at a short-wavelength limit that shifts systematically to shorter wavelengths as the electron energy increases. 

The continuous spectrum is thus characterized by a short-wavelength limit and an intensity distribution. Experiments on other target materials have shown that these characteristics are independent of the target material although the integrated intensity increases with atomic number. (See Equation 1-3.) The continuous spectrum, therefore, results generally from the interaction of electrons with matter. Attempts (none completely successful) have been made to treat this interaction theoretically by both classical and quantum mechanics. 

The short-wavelength limit of the continuous spectrum is clearly a quantum phenomenon. X-ray generation by electron bombardment in principle resembles cathodoluminescence, and both processes are inverse photoelectric effects. The short-wavelength limit, Xq, discovered by Duane and Hunt6 obeys the relationship... 

Xo being the short-wavelength limit (1.5). The sharpest curve in Figure... 

If the experiment to which the calculation refers were actually attempted, several differences would appear. A lost important, the x-ray power would be expended over a vide spectrum. The intensity in Equation-4-10 would be the integrated intensity from the short-wavelength limit to the critical absorption wavelength. /Also, gmax and wka would need to be replaced by values that reflect the wavelength range of the integrated intensity. The net effect of all these differences would be to reduce /k below the value of Equation 4-16, perhaps by as much as ten-fold. 

The size of the quantum for wavelength 1.60 A is the product of Planck s constant and the corresponding frequency according to the general law of which Equation 1-1 is the special case for the short-wavelength limit. 

The phosphorescence from most dialkyl ketones does not have separated bands so it is difficult to assign a triplet energy as it has been defined here. The maximum of the emission is usually near 4400 A with a short wavelength limit usually < 4000 A (> 71 kcal mole-1). 

Dominated by Iron Absorption. Discernable increases in absorbance (reflectance decreases) are produced by increasing iron content in two wavelength regions - the absorption tail diminishing throughout the uv-visible portion of the of the spectrum (sampled at the short wavelength limit of the spectra) and the broad peak at 970nm. These features are attributable to a series of d-d transitions of ferric and ferrous iron Q4.). ... 

The short-wavelength limit for a photomultiplier is determined by the transmission of the window material covering the photocathode. Quartz can be used for tubes to be operated down to about 170 nm, and tubes with LiF windows are available to permit operation down to 105 nm. In the 30 to 300 nm region, an ordinary photomultiplier can be used by coating the quartz or pyrex entrance window with a film of sodium salicylate that, upon absorption of UV light, fluoresces with nearly unit quantum efficiency at about 400 nm. 

DTA = differential thermal analysis FCC = face centered cubic FWHM = full width at half maximum ICDD = international center for diffraction data JCPDS = joint committee on powder diffraction standards EP = Lorentz and polarization PO = Preferred orientation. PT = parallel tempering PXRD = powder X-ray diffraction SA = simulated annealing SWE = short-wavelength-limit TGA = thermogravametric analysis XRPD = X-ray powder diffraction XRD = X-ray diffraction ... 

PC Hobbins and I had in 1950 begun to work on the polarized ultraviolet absorption spectrum of anthracene. We had by that time the use of a quartz Wollaston prism, designed by Dr HG Poole and made by Adam Hilger. It was an important advance, because measurements could be made, one polarized beam at a time, down to a short wavelength limit of about 190 nm. The anthracene solution spectrum shows two absorptions, near 380 nm and near 250 nm. Both are affected by intermolecular forces in the crystal, but could be unravelled to show that the second, very intense, absorption was polarized along the long in-plane molecular axis, in agreement with MO theory. 

The second limit of practical interest is the short wavelength limit uDjV 1 at concentrations far from the onset of stability, when Q 1. It is given by ... 

This equation gives the short-wavelength limit (in angstroms) as a function of the applied vo undergoes... 

Figure 1-12 summarizes some of the relations developed above. This curve gives the short-wavelength limit of the continuous spectrum as a function of applied voltage. Because of the similarity between Eqs. (1-4) and (1-16), the same curve also enables us to determine the critical excitation voltage from the wavelength of an absorption edge. 

Fig. 1-12 Relation between the voltage applied to an x-ray tube and the short-wavelength limit of the continuous spectrum, and between the critical excitation voltage of any metal and the wavelength of its absorption edge.

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