Wavelengths and Energies

The abbreviation sf denotes the number of significant figures in the data. The frequencies, wavelengths, and energies are typical values they should not be regarded as precise. 

This problem relates energies of photons to energy changes of atoms. The solution requires a conversion involving wavelength and energy. 

C07-0107. One frequency of a CB radio is 27.3 MHz. Calculate the wavelength and energy of photons at this frequency. 

The emission spectra of He and reveal transitions at characteristic energies. The emitted photons have different wavelengths and energies because iHe has quantized energy levels that are different from those of l ... 

In XRF, an X-ray beam or gamma rays are used to displace electrons from the inner orbitals of elements. When electrons fall into these orbitals, replacing the removed electrons, photons of specific wavelengths and energy are emitted, detected, and measured to determine which elements are present. The X-rays used in XRF do not penetrate deeply and so elements on the surface of the sample are measured, while those in the interior may not be detected [3],... 

Fig. 7.17. Basic components of the apparatus used for the measurement of X-ray fluorescence by the wavelength and energy dispersive methods.WDX X-rays from the source (A) are allowed to impinge on the sample (B) the resulting XRF is discriminated by the crystal (C), and finally measured by the detector (D). EDX X-rays from the source (A) are allowed to impinge on the sample (B), and the resulting XRF is measured by the detector (D).

R. Jenkins, Comparison of wavelength and energy dispersive spectrometers. In X-Ray Fluorescence Spectrometry, 2nd ed., Wiley-Interscience, New York, 1999, pp. 111-121 Chapter 7. 

An X-ray fluorescence spectrometer needs to resolve the different peaks, identify them and measure their area to quantify the data. There are two forms of X-ray spectrometers (Fig. 5.5), which differ in the way in which they characterize the secondary radiation - wavelength dispersive (WD), which measures the wavelength, and energy dispersive (ED), which measures the energy of the fluorescent X-ray (an illustration of the particle-wave duality nature of electromagnetic radiation, described in Section 12.2). 

However, in the sodium atom, An = 0 is also allowed. Thus the 3s —> 3p transition is allowed, although the 3s —> 4s is forbidden, since in this case A/ = 0 and is forbidden. Taken together, the Bohr model of quantized electron orbitals, the selection rules, and the relationship between wavelength and energy derived from particle-wave duality are sufficient to explain the major features of the emission spectra of all elements. For the heavier elements in the periodic table, the absorption and emission spectra can be extremely complicated - manganese and iron, for example, have about 4600 lines in the visible and UV region of the spectrum. 

It follows that the x-axis in Figure 1.1 is an energy scale, since the frequency, wavelength and energy of electromagnetic radiation are interrelated ... 

Table 1.1 Equivalence oiirequency. wavelength and energy units for electromagnetic radiation...

Figure 9-7 The span of the spectrum of electromagnetic radiation used in spectroscopic investigations of organic compounds along with comparison of some of the various units commonly employed for wavelength and energy of the radiation on log scales...

Because of the inverse proportionality between wavelength and energy, the relationship may be written as... 

Table 3.1. Wavelength and energy units used in crystal field spectra...

UV radiation comprises energies from about 300 kJ Einstein-1 (UV-A radiation, 1 einstein= 1 mol of photons), up to 1200 kJ Einstein-1 (vacuum UV). Table 6 shows the wavelength and energy of dilferent UV radiation types. 

Electron microprobes permit chemical microanalysis as well as SEM and BSE detection, often referred to as analytical electron microscopy (AEM), or electron probe microanalysis (EPMA)56 57. This is because another product of the surface interaction with an incident electron beam is X-ray photons which have wavelengths and energies dependent on element identity and on the electron shell causing the emission. Analysis of these photons can give a local chemical analysis of the surface. Resolution of 1 pm is attainable. Two types of X-ray spectrometer can be employed ... 

The quoted lifetime is for the v = 0 level, and the wavelength and energy are for the (0, 0) transition unless otherwise stated or unknown. 6 It is possible that the quoted lifetime is actually that of the w state, which cascades to the a state, while the true lifetime of the a state is about 1 x 10-5 sec, as obtained by Jeunehomme (49). 

In Part III of this series titled, "A Light Stability Cabinet for Evaluating the Photosensitivity of Pharmaceuticals," authored by Lachman et al. (38) they discussed the history of photostability testing in allied fields, the different sources that had been used along with their benefits and short-comings, and the rationale for the source they selected. The authors also presented some of the basic theory involved in this field, e.g., the relationship between wavelength and energy. 

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