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In organic chemistry, free-radical addition is an addition reaction which involves free radicals. Radical additions are known for a variety of unsaturated substrates, both olefinic or aromatic and with or without heteroatoms. Free-radical reactions depend on one or more relatively weak bonds in a reagent. Under reaction conditions (typically ...
Lewis dot structure of a Hydroxide ion compared to a hydroxyl radical. In chemistry, a radical, also known as a free radical, is an atom, molecule, or ion that has at least one unpaired valence electron. [ 1][ 2] With some exceptions, these unpaired electrons make radicals highly chemically reactive. Many radicals spontaneously dimerize.
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
In mathematics, a sum of radicals is defined as a finite linear combination of n th roots: =, where , are natural numbers and , are real numbers.. A particular special case arising in computational complexity theory is the square-root sum problem, asking whether it is possible to determine the sign of a sum of square roots, with integer coefficients, in polynomial time.
The chemical basis for Markovnikov's Rule is the formation of the most stable carbocation during the addition process. The addition of the hydrogen ion to one carbon atom in the alkene creates a positive charge on the other carbon, forming a carbocation intermediate. The more substituted the carbocation, the more stable it is, due to induction ...
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The hydroxyl radical, •HO, is the neutral form of the hydroxide ion (HO – ). Hydroxyl radicals are highly reactive and consequently short-lived; however, they form an important part of radical chemistry. Most notably hydroxyl radicals are produced from the decomposition of hydroperoxides (ROOH) or, in atmospheric chemistry, by the reaction ...
Plot of the Bring radical for real argument. In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial + +.. The Bring radical of a complex number a is either any of the five roots of the above polynomial (it is thus multi-valued), or a specific root, which is usually chosen such that the Bring radical is real-valued for real a and is an ...
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