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Electrical Aspects
Published in Frank R. Spellman, The Science of Wind Power, 2022
It was stated earlier that in an atom the number of protons is usually the same as the number of electrons. This is an important point because this relationship determines the kind of element (the atom is the smallest particle that makes up an element; an element retains its characteristics when subdivided into atoms) in question. Figure 8.3 shows a simplified drawing of several atoms of different materials based on the conception of electrons orbiting about the nucleus. For example, hydrogen has a nucleus consisting of one proton, around, which rotates one electron. The helium atom has a nucleus containing two protons and two neutrons with two electrons encircling the nucleus. Both of these elements are electrically neutral (or balanced) because each has an equal number of electrons and protons. Since the negative (−) charge of each electron is equal in magnitude to the positive (+) charge of each proton, the two opposite charges cancel.
Petroleum Pre-Period
Published in Muhammad Abdul Quddus, Petroleum Science and Technology, 2021
Any chemical reaction, including a nuclear reaction, depends on the number of factors prevailing in the environment. All elements are produced in the universe through nuclear reactions. In the first few minutes after the Big Bang, during the radiation era, two light, stable gas elements, hydrogen and helium, were produced by the integration of fundamental particles. Hydrogen (11H) was produced by the combination of one proton and one election. A helium atom consists of two protons, two neutrons and two electrons (42H). The majority of elements were produced during the ‘star cycle’ in a galaxy. From the initial stage of star formation till the final stage of ‘supernova’ explosion, is a long duration of time, billions of years. In the duration, different conditions of temperature, density and radiation occur, so that several different kinds of elements are produced. The diffuse mass of radiations, atoms and ions in the universe progressively turned into a compact, dense, hotter spherical mass, creating ideal conditions for nuclear reactions to take place. Hydrogen and helium atoms were the first to be created; therefore, these are to be first consumed by hydrogen and helium nuclear reactions. Two main nuclear reactions, nuclear fission and nuclear fusion, are responsible for the generation of the elements.
Exact matrix elements for general two-body central-force interactions, expressed as sums of products
Published in Molecular Physics, 2019
Jonathan Jerke, Jacek Karwowski, Bill Poirier
The 6D Schrödinger equation for two interacting particles confined in an external potential (e.g. the helium atom) is, in general, not separable. On the other hand, an important class of exceptions was discovered by Kestner and Sinanoğlu, already more than half a century ago [44]. In particular, they showed that when the two particles interact via a central force potential, and the external confining potential is harmonic, then the 6D problem rigorously separates into two 3D problems. Each of the latter, moreover, individually adopts the usual central-force form – meaning that they in turn separate into radial and angular components that can be solved individually. The entire problem, in other words, becomes completely separable.