Matter dual nature

In 1923 de Broglie made the bold suggestion that matter, like light, has a dual nature in that it sometimes behaves like particles and sometimes like waves. He suggested that material (i.e., non-zero-rest mass) particles with a momentum p = mv should have wave properties and a corresponding wavelength given by... 

Electromagnetic radiation can be absorbed or emitted. The absorption of ultraviolet radiation by our skin may cause sunburn. When we cook food in a microwave oven, the absorption of microwave radiation by the water in the food causes the water molecules to vibrate, generating heat that cooks the food. However, when electromagnetic radiation is absorbed or emitted by matter, it behaves more like a stream of particles than as a wave motion. These particles are called photons and so electromagnetic radiation can be considered both as a stream of photons and as waves with characteristic properties, such as wavelength (1) and frequency (/). Therefore we say that electromagnetic radiation has a dual nature wave motion and streams of photons. 

A class of partial differential equations first proposed by Erwin Schrodinger in 1926 to account for the so-called quantized wave behavior of molecules, atoms, nuclei, and electrons. Solutions to the Schrodinger equation are wave functions based on Louis de Broglie s proposal in 1924 that all matter has a dual nature, having properties of both particles and waves. These solutions are... 

The possibility that the propagation of fight could have a dual nature arose in the seventeenth century as a controversy between Newton and Huygens corpuscular versus undulatory descriptions, respectively. When Maxwell s electromagnetic theory was developed in the nineteenth century, the matter seemed settled in favor of the proponents of wave-like electromagnetic phenomena. 

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... 

The Heisenberg Uncertainly Principle arises from the dual nature (wave-particle) of matter. It states that there exists an inherent uncertainty in the product of the position of a particle and its momentum, and that this uncertainty is on the order of Planck s constant. 

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. 

Explain the statement. Matter and radiation have a dual nature. ... 

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... 

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