What is Radical: Definition and 162 Discussions

In chemistry, a radical is an atom, molecule, or ion that has an unpaired valence electron.
With some exceptions, these unpaired electrons make radicals highly chemically reactive. Many radicals spontaneously dimerize. Most organic radicals have short lifetimes.
A notable example of a radical is the hydroxyl radical (HO·), a molecule that has one unpaired electron on the oxygen atom. Two other examples are triplet oxygen and triplet carbene (꞉CH2) which have two unpaired electrons.
Radicals may be generated in a number of ways, but typical methods involve redox reactions. Ionizing radiation, heat, electrical discharges, and electrolysis are known to produce radicals. Radicals are intermediates in many chemical reactions, more so than is apparent from the balanced equations.
Radicals are important in combustion, atmospheric chemistry, polymerization, plasma chemistry, biochemistry, and many other chemical processes. A majority of natural products are generated by radical-generating enzymes. In living organisms, the radicals superoxide and nitric oxide and their reaction products regulate many processes, such as control of vascular tone and thus blood pressure. They also play a key role in the intermediary metabolism of various biological compounds. Such radicals can even be messengers in a process dubbed redox signaling. A radical may be trapped within a solvent cage or be otherwise bound.

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  1. C

    Atom-Transfer Radical Polymerization: Method Question

    Hi everyone, So I'm a chemical engineering grad student and oddly enough I have been tasked with doing chemistry (strange I know). I'm currently doing atom-transfer radical polymerization (ATRP) using a metal (CuCl or CuBr) and a ligand (dNbpy or PDMETA). My monomer is a methacrylate group...
  2. A

    Automorphism Group of Radical of Finite Group

    I am working on a problem on automorphism group of radical of finite group like this one: Here are what I know and what I don't know: ##Aut(R(G))## is an automorphism group, whose elements consist of isomorphic mappings from ##R(G)## to itself. For visualization purpose, I envision the...
  3. nuuskur

    Antiderivative involving a radical

    Homework Statement \int\frac{1}{(x+1)^2}\sqrt{\frac{x}{1-x}}{\rm{d}}x Homework EquationsThe Attempt at a Solution Utterly perplexed. Have no ideas how to do this one. Did try bringing the entire thing under square root and try partial fractions, but the entire thing is modified by the square...
  4. iamjon.smith

    Complex Radical or Complex Root?

    solve a radical expression: 1.5r250 (*r denotes the radical symbol) in a radical expression where the index of the root is 1.5 and the number is 250 Use Calculator, Show Steps Homework Equations The Attempt at a Solution First of all, using a calculator the answer comes out to 39.685, but I...
  5. O

    Radical with negative radicand squared

    Can someone explain this for me. sqrt x^2 = x (sqrt x)^2 = x Yet sqrt -1^2 = |x| = -(-1) = 1 (sqrt -1)^2 = (sqrt -1)(sqrt -1) = -1
  6. E

    Derivative of a fraction inside a radical

    f(z) = sq. rt of z-1 / z+1 --- both numerator and denominator are inside the radical. I can write it as (z-1)^1/2 over (z+1)^1/2, right? If I simplify it using derivative of a quotient. Should I simplify (z-1)^1/2 and (z+1)^1/2 as whole numbers and multiply them to other terms, including...
  7. marcus

    Radical new cosmic model (Barrau Linsefors one-up Penrose)

    ==from conclusions section on page 4 of Barrau Linsefors June paper== V. REBIRTH OF THE UNIVERSE AND TESTS OF THE MODEL In the far future, huge patches of our universe, with radii larger than the Hubble scale, will be completely empty. They will be pure dS spaces. If the model suggested in this...
  8. paulmdrdo1

    MHB Radical Equation Solution: Simplifying and Transposing for Accurate Results?

    $\sqrt{x}-\frac{2}{\sqrt{x}}=1$ transposing $\frac{2}{\sqrt{x}}$ to the right-side $\sqrt{x}=\frac{2}{\sqrt{x}}$ multiply by $\sqrt{x}$ I get, $x=2$ is my solution correct? if not please explain why. thanks!
  9. I

    Is it okay to use dot/cross for free radical rxns

    I'm learning about various radical reactions, the thing is I'm still getting my head around 'half arrow' mechanisms. However for some reason the dot and cross model for these types of reactions is really intuitive and works great for my understanding. Is this a dangerous path to go down, to work...
  10. caters

    Free Radical reaction of methane and Chlorine

    Homework Statement Lets say you have 1 liter of 2 mol/L methane and the same amount of chlorine. Let's also say that both are liquids since those are most likely to react. Now the only way they can both be liquids is if the temperature is as cold as an antarctic winter so this is not aqueous...
  11. S

    Cyclohexene radical isomers stability

    The enthalpies of creating a cyclohexene radical isomers are: ORTHO: 444 kJ/mol META: 361 kJ/mol PARA: 401 kJ/mol The meta-isomer is most stable (that is the reason for the formation of meta product in radical addition). Para/meta isomers energies seem obvious - both carbons...
  12. Sudharaka

    MHB Ring Epimorphism and Nil Radical

    Hi everyone, :) Here's a question that I failed to do correctly in an exam. I want to find the answer to this and understand it fully. Any comments, hints would be greatly appreciated. Question: If $\theta:\, R\rightarrow S$ is a ring epimorphism, prove that \(\theta(\mbox{Nil }(...
  13. Albert1

    MHB How to Simplify Radical Expressions with Multiple Radicals?

    simplify: $\sqrt {21-4 \sqrt 5 +8\sqrt 3 - 4\sqrt {15}}$
  14. Tyrannosaurus_

    Limit of a function with a radical in numerator

    Homework Statement Evaluate the limit as x → 0 (zero), if it exists, for: [(x+4)^(1/2) - 2]/xThe Attempt at a Solution I was not too sure at an elegant solution because nothing like this existed in the coursework. The best I could think of was to evaluate the limit on each side of zero. I...
  15. B

    MHB Difference Between Two Radicals

    can you tell the difference $\displaystyle \sqrt{(1)^2}=1$$\displaystyle \sqrt{(-1)^2}=-1$
  16. DreamWeaver

    MHB An absurdly interesting radical....

    Here's an interesting limit I found the other day...\text{limit}_{\, \epsilon \to 0^{+}}\sqrt{\epsilon + \sqrt{\epsilon + \sqrt{ \epsilon + \sqrt{\epsilon + \cdots} } } } = 1It's both obvious and yet elusive... Any ideas on how to prove it...?
  17. K

    Integration of a complicated radical function

    Homework Statement ∫(√x).[√(x+1)] dx Homework Equations The Attempt at a Solution Sorry but i couldn't get it any far than this u substitutionu = √(x+1) du = [(1)/{2√(x+1)}]dx → dx = [2√(x+1)]du putting in the main expression∫ √(u2 - 1). 2u2 du
  18. T

    MHB Root Calculation: Isolating the Radical

    Re: Root calculations How would you isolate the radical in this example: n(\sqrt{n^2+4)}-n^2
  19. A

    How to perform an integral with a polynomial and a radical?

    Homework Statement Homework Equations The Attempt at a Solution How did they go from the first step in the blue to the second step in the blue? I tried integration by parts but that didn't work.
  20. D

    Simplified Radical Form with square and cubed roots

    I just got a new Ti-nspire Cx CAS calculator and I am having trouble with being able to express a Radical in simplified form when there are exponents and variables of x and y. My problem is that this calculator will not show the simplified form correctly. I have taken others advice in setting...
  21. C

    Radical Equation Restrictions & Solution | Sqrt 5x2 +11= x+5 Homework

    Homework Statement Sqrt 5x2 +11= x+5 State the restrictions for x and solve. Homework Equations 5x2+11 ≥ 0 x2≥-11/5 (then how can u take the sqrt of a negative number??) The Attempt at a Solution The answer at the back of the book is 7/2, -1 I don't know what...
  22. J

    Free radical polymerization

    Does branching occur during free radical polymerization of ethylene even at high temperatures and pressure or only on other type of monomers using free radical polymerization at lower temperatures? I was reading this article: http://en.wikipedia.org/wiki/Polymerization It was not very...
  23. N

    How to simplify double radical when theres fractions involved?

    Homework Statement sqrt((2-sqrt(3))/4) I tried to split whatever is under the radical sign into two separate parts, 1/2 and (-1/4)sqrt(3) I realized that 1.5 times 2 is 3 and 2-1.5 = 1/2 so it seemed like it fulfilled the requirements for solving a double radical. so I put down...
  24. M

    Understanding the Convergence of Radical Functions

    This is something that comes up when I want to determine whether the sequence of functions {f_n} converge uniformly to f: Suppose f_n(x) = sqrt(x^2 + 1/n^2), so f(x) = x. Then, according to Spivak, f(x) - f_n(x) = sqrt(x^2) - sqrt(x^2 + 1/n^2) = 1/(2n^2*sqrt(ε)) for some ε such that x^2 < ε...
  25. marcus

    Radical new foundations for both quantum theory and space-time

    This was just posted http://arxiv.org/abs/1308.2206 Energetic Causal Sets Marina Cortês, Lee Smolin (Submitted on 9 Aug 2013) We propose an approach to quantum theory based on the energetic causal sets, introduced in Cortês and Smolin (2013). Fundamental processes are causal sets whose...
  26. M

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  27. Z

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  28. R

    Why doesn't this radical equation have a solution?

    I don't understand why this is a no solution original problem √(x-5) - √(x-8) = 3 My solution attempt add +√(x-8) to both sides: √(x-5) - √(x-8) = 3 √(x-5) = 3 + √(x-8) squaring both sides: (√(x-5))^2 = (3 + √(x-8))^2 FOIL out the right side: x - 5 = 3^2 +...
  29. C

    Mobile v. Adsorbed Hydroxyl Radical

    In the linked article, http://pubs.acs.org/doi/abs/10.1021/jp036735i the authors describe the generation of "free" or "mobile" OH radicals on surface fluorinated TiO2, \text{Ti}-\text{F}+\text{H}_2\text{O}~(\text{or }\text{OH}^-)+h_\text{vb}^+\longrightarrow...
  30. O

    Radical and its rational exponential form

    Can someone explain how these are equivalent. sqrt((-3)^2) = (-3)^2/2 =sqrt(9) and (-3)^1 3 is not equal to -3 (-3)^2/2 can be expressed as: (-3^2)^1/2 and (-3^1/2)2 (9)^1/2 and (sqrt(-1)sqrt(3))^2...
  31. anemone

    MHB Determine all real x for a given radical equation.

    Determine all real x satisfying the equation \sqrt[5]{x^3+2x}=\sqrt[3]{x^5-2x}
  32. marcus

    Radical new take on *uni*verse questions by Smolin, could be important

    Smolin has a new book (Time Reborn) coming out this month. Amazon has a page on it, with advance reviews. He gave a talk on the main ideas at Perimeter in February. I was impressed by the depth and cogency. It is a 60 minute talk followed by a lengthy discussion with Rob Myers, Laurent Freidel...
  33. anemone

    MHB How to Simplify Nested Radicals?

    Simplify \sqrt{1+a^2+\sqrt{1+a^2+a^4}}.
  34. W

    Can This Integral Be Solved Using Factoring and Substitution?

    Homework Statement evaluate the integral.Homework Equations \displaystyle\int {\frac{3x+2}{\sqrt{1-x^2}} dx}The Attempt at a Solution - i tried factoring hoping for a perfect square that i could take the square root of, but that doesn't work. -u-sub won't work: u=1-x^2 ; du=2x -i don't know...
  35. M

    Proof/Show with polynomials under the radical

    Homework Statement show that: \sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=2 Homework Equations I remember over-hearing someone talking about the modulus? I don't know how that's suppose to help me The Attempt at a Solution I'm still at the conceptual stage :cry: I don't know which...
  36. anemone

    MHB How to Solve a Complex Radical Equation?

    Problem: Solve for x in the following equation: $\sqrt{x+\sqrt{x+11}}+\sqrt{x+\sqrt{x+-11}}=4$ I have not attempted this particular problem simply because I haven't the faintest idea how to even start it... Could anyone please give me some hints on how to approach it, please? Many thanks in...
  37. S

    Max number of roots of radical equation

    I am doing some independent study and appreciate that a polynomial (in x) of integer degree (n) can have at most n roots; many proofs to this effect exist. My query concerns the number of roots of equations in which the powers of x are not integers (or rational numbers) but irrational...
  38. A

    Finding simplest radical form of a 4th root?

    I haven't taken math in years and am having trouble understanding how to find simplest radical form of a 4√(x14). I said x4√x10. I realize I have 3 x4ths and x2 but I'm not sure if I can pull out more xs. What are the rules for this? Ideas, insight?
  39. P

    Closed form of an infinitely nested radical.

    Hello. Does anybody happen to know a closed form of this infinitely nested radical? http://imageshack.us/a/img268/6544/radicals.jpg By any chance, maybe you even saw it somewhere? I haven't had too much success so far. At the moment I am so desperate that I'm even willing to try and...
  40. H

    What is a Radical? Exploring Continuity of a Bizarre Function

    I'm currently writing a proof that relates to continuity of a bizarre function and I ran across an interesting thought, at least to me. I don't really know what a radical √ is. For example, 6^3 is: 6*6*6 and x^n is: x*x*x*x*x*x*x*x*x*x, n times, but what is a square root (ie...
  41. karush

    MHB *oblique asymptotes of radical expressions

    it seems most oblique asymptotes are mostly with rational expressions but $\sqrt{x^2+6x}$ has the asymptote of $y=x+3$ and $y=-x-3$ I don't know how this is derived since it is not a rational expression thanks ahead:cool:
  42. I_am_learning

    Finding general solution of Radical Equation

    Before trying to find out the general solution of a radical equation; I would first like to know if it can be found? For example I have a equation of the form \text{A1}+\text{A2} x + \text{A3}\sqrt{\text{B1}+\text{B2} x+\text{B3} x^{\frac{3}{2}}+\text{B4}\sqrt{x}+\text{B5} x^2}+...
  43. D

    System of two equations with radical expression

    Homework Statement I am trying to solve the following two systems of equations and at every attempt I get completely stuck. x2 + y2 = 1 -x + √3y = 0Homework Equations not applicableThe Attempt at a Solution the answers have already been given to me but I have no idea how to get the answers...
  44. C

    MHB How Do You Identify Scalar Homomorphisms in a Matrix Algebra?

    Let M be the set of 2x2 matrices defined by M = {a b 0 d} where a, b and d are complex. I've found a basis for M but need to know how to find the set of scalar homomorphisms of M from these. I have the basis as M_1 = {1 0 0 1} M_2 = {0 1 0 0} and M_3 = {0 0...
  45. B

    Radical of the annihilator is the intersection of associated primes

    1. Homework Statement R,M are Noetherian. Prove that the radical of the annihilator of an R-moduleM, Rad(ann(M)) is equal to the intersection of the prime ideals in the set of associated primes of M (that is denoted so regretfully that I am not even allowed to spell it out by the system)...
  46. A

    Simplifying radical in a radical

    How would you approach something like this? \sqrt{-\sqrt{3}+\sqrt{4+\sqrt{5}+\sqrt{17-4\sqrt{15}}}}
  47. A

    How Do Radical Ideals Relate to Submodules in Algebra?

    I'm currently studying commutative algebra/algebraic geometry out of Cox Little and O'Shea's Ideal Varieties and Algorithms, and linear algebra out of Steven Roman's Advanced Linear Algebra. In Roman, I'm learning about modules, and I have a question about the relationship between these two...
  48. D

    Multiplying Radical expression clarification

    Homework Statement This isn't really a specific question, I just need clarification on multiplying a radical expression If I were to do... x multiplied by 4√6, which number would receive the variable x when multiplied? Homework Equations The Attempt at a Solution
  49. I

    Galois Theory - Question about Radical Extensions

    Homework Statement Suppose that I\subseteq J are subfields of \mathbb{C}(t_1,...,t_n) (that is, subsets closed under the operations +, - , \times, \div), and J is generated by J_1,...,J_r where I \subseteq J_j \subseteq J for each j and J_j:I is radical. By induction on r, prove that J:I is...
  50. G

    Integral of expression with radical

    Homework Statement There's a problem that involves triple integrals, but basically, I've boiled all of it down to the following single integral but cannot proceed any further. ∫u2 sqrt(a2-u2) du from 0 to a where a is a constant Homework Equations The Attempt at a Solution I attempted to use...
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