Dual nature of matter

Acceptance of the dual nature of matter and energy and of the uncertainty principle culminated in the fi eld of quantum mechanics, which examines the wave nature of objects on the atomic scale. In 1926, Erwin Schrddinger derived an equation that is the basis for the quantum-mechanical model of the hydrogen atom. The model describes an atom that has certain allowed quantities of energy due to the allowed frequencies of an electron whose behavior is wavelike and whose exact location is impossible to know. 

The German physicist Werner Heisenberg ( FIGURE 6.14) proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and... 

The German physicist Werner Heisenberg ( Figure 6.15) proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of an object at a given instant. The limitation becomes important only when we deal with matter at the subatomic level (that is, with masses as small as that of an electron). Heisenberg s principle is called the uncertainty principle. When appHed to the electrons in an atom, this principle states that it is impossible for us to know simultaneously both the exact momentum of the electron and its exact location in space. 

For improved magnification, one exploits the dual nature of matter, that particles also behave as waves. The wavelengths are obtained from the momentum as mV = TjihlX, where m is the mass of the particle, Vis its velocity, h is Planck s constant, and k is the resulting wavelength. For electrons, the wavelength works out to be about 0.005 nm, calculated resolution 0.003 nm, and the aetual resolution more like 2 nm. Since electric and magnetic fields can be used like lenses, unlike... 

The miderstanding of molecular motions is necessarily based on quaiitum mechanics, the theory of microscopic physical behaviour worked out in the first quarter of the 20th century. This is because molecules are microscopic systems in which it is impossible—or at least very dangerous —to ignore the dual wave-particle nature of matter first recognized in quaiitum theory by Einstein (in the case of classical waves) and de Broglie (in the case of classical particles). 

Electromagnetic radiation, which was previously thought to exhibit only wave properties, seems to show certain characteristics of particulate matter as well. This phenomenon, illustrated in Fig. 12.6, is sometimes referred to as the dual nature of light. 

In relation to the basically dual nature of the charging process, we have two possible ways of identifying the p.z.c. as pAg° or pl° for silver iodide, as pH° or pOH° for oxides, etc. It is customary to choose the first option and we shall follow this usage, but this is not a matter of principle. The two are related by... 

Other phenomena are best described in terms of light s particle nature (Equation 1.4). These seemingly contradictory properties are inseparable parts of the dual nature of light. Both must be taken into account when considering a simple process such as the absorption of light by matter. The above statements will surprise few readers because they have heard them many times before. But consider the experiment depicted in Figure 1.7. 

The truth is that both matter and energy show both behaviors each possesses both faces. In some experiments, we observe one face in other experiments, we observe the other face. The distinction between a particle and a wave is meaningful only in the macroscopic world, not in the atomic world. The distinction between matter and energy is in our minds and our limiting definitions, not inherent in nature. This dual character of matter and energy is known as the wave-particle duality. 

Based on dual particle and wave nature of matter... 

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