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Radical elimination can be viewed as the reverse of radical addition. In radical elimination, an unstable radical compound breaks down into a spin-paired molecule and a new radical compound. Shown below is an example of a radical elimination reaction, where a benzoyloxy radical breaks down into a phenyl radical and a carbon dioxide molecule. [7]
In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product: r a d ( n ) = ∏ p ∣ n p prime p {\displaystyle \displaystyle \mathrm {rad} (n)=\prod _{\scriptstyle p\mid n \atop p{\text{ prime}}}p}
A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.).
A radical ideal (or semiprime ideal) is an ideal that is equal to its radical. The radical of a primary ideal is a prime ideal . This concept is generalized to non-commutative rings in the semiprime ring article.
For example, when polystyrene decomposes upon heating at a temperature above 300 °C, a styrene monomer is generated via a radical elimination mechanism (See Fig. 2). [2] Here, the new radical is generated on the polymer chain, which can further undergo a similar type of reaction to generate more styrene molecules.
an organic compound; simplest example of the ketones: Acetylene: a hydrocarbon and the simplest alkyne; widely used as a fuel and chemical building block Ammonia: inorganic; the precursor to most nitrogen-containing compounds; used to make fertilizer Ammonium hydroxide: aqueous ammonia; used in traditional qualitative inorganic analysis
The basic steps in any free-radical process (the radical chain mechanism) divide into: [2] Radical initiation: A radical is created from a non-radical precursor. Chain propagation: A radical reacts with a non-radical to produce a new radical species; Chain termination: Two radicals react with each other to create a non-radical species
A general acyl group (blue) in a ketone (top left), as an acylium cation (top centre), as an acyl radical (top right), an aldehyde (bottom left), ester (bottom centre) or amide (bottom right). ( R 1 , R 2 and R 3 stands for organyl substituent or hydrogen in the case of R 1 )