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The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .
The charge number equals the electric charge (q, in coulombs) divided by the elementary charge: z = q/e. Atomic numbers (Z) are a special case of charge numbers, referring to the charge number of an atomic nucleus, as opposed to the net charge of an atom or ion. The charge numbers for ions (and also subatomic particles) are written in ...
Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge. Thus, an object's charge can be exactly 0 e, or exactly 1 e, −1 e, 2 e, etc., but not 1 / 2 e, or −3.8 e, etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.)
The charge number of an atomic nucleus was found to be equal to the element's ordinal position on the periodic table. The nuclear charge number thus provided a simple and clear-cut way of distinguishing the chemical elements from each other, as opposed to Lavoisier's classic definition of a chemical element being a substance that cannot be ...
Euler's great interest in number theory can be traced to the influence of his friend in the St. Peterburg Academy, Christian Goldbach. A lot of his early work on number theory was based on the works of Pierre de Fermat, and developed some of Fermat's ideas. One focus of Euler's work was to link the nature of prime distribution with ideas in ...
Then each base a corresponds to an inverse function called the logarithm to base a, in chapter 6. In chapter 7, Euler introduces e as the number whose hyperbolic logarithm is 1. The reference here is to Gregoire de Saint-Vincent who performed a quadrature of the hyperbola y = 1/x through description of the hyperbolic logarithm. Section 122 ...
Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər; [b] German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] ⓘ, Swiss Standard German: [ˈleɔnhard ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of ...
A system of one or more electrons bound to a nucleus is called an atom. If the number of electrons is different from the nucleus's electrical charge, such an atom is called an ion. The wave-like behavior of a bound electron is described by a function called an atomic orbital. Each orbital has its own set of quantum numbers such as energy ...