b. With the interstitial mechanism, one atom is usually much smaller than the other, so cannot successfully replace an atom in the crystals of the base metal. In which of the following processes are covalent bonds broken? Carbon gives strength and hardness but at the expense of ductility. Find answers to questions asked by students like you. which of the following correctly indicates whether the solid represented by the particle model shown to the left conducts electricity and explains why or why not? (D) Cl2O As we discussed earlier shows the viewing screen in a double-slit experiment with monochromatic light. Chemical Engineering questions and answers. Engineers apply the knowledge of math & science to design and manufacture maintainable systems used to solve specific problems. AskEngineers is a forum for questions about the technologies, standards, and processes used to design & build these systems, as well as for questions about the engineering profession and its many disciplines. 2. steel is an alloy containing fe atoms and c atoms. 200 For further information regarding Particle structure of alloys, kindly refer, This site is using cookies under cookie policy . Start your trial now! C) sp3 sp3, The atom that contains exactly two unpaired electrons. (E) CaCl2, According to the VSEPR model, the progressive decrease in the bond angles in the series of molecules CH4, NH3, and H2O is best accounted for by the C) CuCl III. the diagram above shows two resonance structures for a molecule of C6H6. Transcribed Image Text: Steel is an alloy containing Fe atoms and C atoms. It can keep a sharp cutting edge. This is because this nail is an alloy of iron with carbon, chromium and nickel. (b) The atomicmasses of 6Li and 7Li are 6.015122 and 7.016004 amu, respectively.A sample of lithium depleted in the lighter isotopewas found on analysis to contain 1.442% 6Li. We tested it and wrote it down. O = Fe Which, Q:The name given to the elements How can a kitchen knife be A2 steel at room temperture (22C)? The smaller atoms become trapped in the spaces between the atoms in the crystal matrix, called the interstices. We found that results could be replicatable if the constants could be held true. 1. CCl4, CO2, PCl3, PCl5, SF6 Which of the following does not describe any of the molecules above? unlike BF3, NF3 has a polar geometry due to an unshared pair of electrons on the N atom. Steel is an interstitial alloy that is made of carbon and iron. N Please select which sections you would like to print: Metallurgical consultant. Give the electron configuration for the following atoms using appropriate noble gas inner 3. Floreal International Ltd, neutrons Which of the following is a nonpolar molecule that contains polar bonds? Steel is an alloy containing Fe atoms and Catoms. Image Based Life > Uncategorized > steel is an alloy containing fe atoms and c atoms. Beyond that, you can also see that there are many phases of steel availible with different temperature / carbon concentrations. C) Cl2 Fe, Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell, Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer, Spencer L. Seager, Michael R. Slabaugh, Maren S. Hansen, John C. Kotz, Paul M. Treichel, John Townsend, David Treichel, Steel is an alloy containing Fe atoms and C atoms. Consider the atomic radii of both carbon and iron and draw a model that describes the alloy that forms. Are there any use cases for alloys with a very high carbon content? C. O The nucleus of 6Li is a powerful absorber of neutrons. for which of the following pairs of ions is the energy that is required to sperate ions largest, steel is an alloy containing Fe atoms and C atoms. (C) PCl3 The A-B-C line represents the liquidus points (i.e., the temperatures at which molten iron begins to solidify), and the H-J-E-C line represents the solidus points (at which solidification is completed). a. Even though carbon, a nonmetal, is a crucial component of steel, the constituents of alloys are typically themselves metals. Enter the chemical symbol, A:Explanation to the correct answer is given below, Q:24. What is the energy change (in J) and wavelength (in nm) of light emitted when an electron, A:The wavelength of hydrogen is given as; (B) Sc, Ti, V2+ This gives us the only possible answer B. Itexists in the naturally occurring metal to the extent of7.5%. Answer: Option A, C is rejected because there is no chromium atom neither in surface nor in the interior side. Steel is made by heating and melting iron ore in furnaces. This is the maximum solubility of carbon in austenite, anything above that and you will have carbides or graphite at all points during the solidification process and there is no heat treat possible that removes them. The following is an electron transfer reaction between two atoms: E) SF6, Which of the following molecules has the shortest bond length? 5 electrons The low carbon content in steel gives it desirable properties such as ductility, toughness, and malleability, making it suitable for a wide range of applications. Reveal answer. Please contact the submission author. Carbon steel contains 2.0% carbon or less, with small amounts of manganese, sulfur, phosphorus, and silicon. N E) I2, For which of the following molecules are resonance structures necessary to describe the bonding satisfactorily? III. DETAILS C) OF Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. based on this information, which of the following diagrams best represent an alloy containing only copper and zinc atoms. What are the most important alloys today? As an indication of the relative importance of this material, in 2013 the worlds raw steel production was about 1.6 billion tons, while production of the next most important engineering metal, aluminum, was about 47 million tons. (E) A metallic solid Q:What is the largest order of any element in U(900)? Omitting very extreme cases, iron in its solid state is, like all other metals, polycrystallinethat is, it consists of many crystals that join one another on their boundaries. ALLOYING ELEMENTS IN STAINLESS STEEL Carbon is a non-metallic element, which is an important alloying element in all-ferrous metal based materials. a) N-3 or F-1 a. Composition of 100 g of carbon steel; element % mass (g) = % mass of steel (g) carbon : 1%: Atoms in a metal are packed tightly in layers and held by strong metallic bonds. Steel is an interstitial alloy made from Carbon and iron atoms. Can be deposited from Austenite as it cools. Assume that the atoms are in the ground state. %%EOF On the basis of coulombs law. Figure 6.7B.1: Different atomic mechanisms of alloy formation, showing pure metal, substitutional, and interstitial structures. 11. Nevertheless, in terms of a multicomponent alloy, atoms whose energy state is affected least by the surface are segregated to the liquid surface region. Which of the following states that the electrons in an atom fill lower- How many resonance structures can be drawn for O3? Let us know if you have suggestions to improve this article (requires login). 3) a single pearlite module is the smallest whole number of iron and carbon atoms that together represent 0.83% carbon. (A) S8 In general, alloy steel is steel that is alloyed with a variety of elements in total amounts between 1.0% and 50% by weight to improve its mechanical The carbon atoms can take up two positions. The carbon atoms can take up two positions. 7.2x13.5x2=16.0,14.4x1+7.0x2=31.07.2x_1-3.5x_2=16.0, -14.4_x1+7.0x_2=31.0 The alloy contains different-sized atoms that make it difficult for the layers to slide over each other. endstream endobj startxref what is the hybridization of the carbon atoms in a molecule of ethyne, represented above? This is why you see red hot steel dunked in water after being worked, although now a days I believe most steel is forced air quenched. with outer-shell electronic Which of the following elements combines with oxygen to form a covalent network solid? Carbon atoms fill the spaces between iron atom, making the structure % more rigid. The lithium metal remaining afterremoval of 6Li was sold on the market. Multivalent The higher the temperature above the, However irregular or Course the Steel grains maybe, if they are heated above the, If Steel is "Soaked" at a temperature of over. D) O2 (A) SiCl4 Although there are thousands of grades of steel, we can break them down into four main categories. What will happen to the fringe spacing if the wave- FIGURE 017.8017.8017.8 length of the light is decreased? (A) S2-, K+, Ca2+ The relatively high boiling point of HF can be correctly explained by which of the following? The A-B-C line indicates that solidification temperatures decrease as the carbon content of an iron melt is increased. In general, alloy steel is steel that is alloyed with a variety of elements in total amounts between 1.0% and 50% by weight to improve its mechanical Alloy steel becomes even tougher as other elements like chromium and nickel are introduced. To put it another way, if you have a bunch of ping pong balls inside of a box they will likely stack in a pyramid style formation, one layer will be offset from the next will be offset from the next. The composition of steel is primarily accounted for by iron (usually accounts for at least 75% of the alloys weight). Steel contains atoms of other elements as well as iron. The professor set up a steel wire with a ring hanging in the center. Which of the following claims about the compound that forms the C and Se is most likely to be true? b. (E) decreasing repulsion between hydrogen atoms, (D) increasing number of unshared pairs of electrons. which has the greater bond length, No2- or NO3-? As we said Steel is an interstitial alloy, not a substitutional. For FCC, we have: 1 Through precise control and manipulation of welding parameters for inertia friction-welded Al alloy/steel joints, the transformation of nanoscale interfacial layer from the amorphous to the mixed phase (co-existence of amorphous and crystallised phases) and then to a fully crystallised Fe 2 Al 5 intermetallic compound (IMC) was observed. And, the sequence of all quantum numbers is = 5,1,0,+1/2, Q:Which element has the following configuration:[Xe]6s24f75d1[Xe]6s24f75d1? c. 3s Which of the following statements accounts for the diffrence in polarity of the two molecules? (C) increasing electronegativity of the central atom Please contact the submission author. , pporting your claim about chemical reactions past wbt radio personalities; embassy suites by hilton phoenix biltmore; canton mckinley high school yearbooks; how to show spotify on lock screen pixel (24 points), An open flask is half filled with water at 25C. Steel is an interstitial alloy with much smaller carbon atoms in the spaces between the iron atoms. sequence of 5, 1, 0, +1/2, A:Given that - hWnId~P0 6JQd6=H{NK:]+ 8Q1&e\p If, however, the steel is heated then cooled quickly (quenched) the molecules cannot rearrange and the steel stays A2 to room temp. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. With a carbon content of more than 2 % one speaks of cast iron! Iron has its bcc allotropy below 912 C (1,674 F) and from 1,394 C (2,541 F) up to its melting point of 1,538 C (2,800 F). Carbon is always present in metallic alloys, i.e. 8.38QP, Your question is solved by a Subject Matter Expert. Steel is an interstitial alloy of iron and carbon that contains between 0.002% and 2.1 % (m/m) of carbon. The Constitution Of Iron Carbon Alloys. President, Historical Metallurgy Society, London, 198486. Press J to jump to the feed. In stainless steel, the atoms are all iron. Today, the most important are the alloy steels, broadly defined as steels containing significant amounts of elements other than iron and carbon. Which of the following diagrams best represents the particle-level structure of steel? The driving power for pitting corrosion is the depassivation of a small area, which becomes anodic (oxidation reaction) while an unknown but potentially vast area becomes cathodic (reduction reaction), leading to very localized galvanic corrosion. In ground state 2A group, there is no unpaired electron. B For alloys below 1.8% Carbon each alloy has a range of temperatures over which freezing takes place but the final liquid does not reach eutectic composition and the construction of the solid alloy is entirely Austenite solid solution. convention on the rights of the child citation oscola; fran finney net worth; cia gateway experience documents; landstar agent salary; torture a ragdoll; There is also the term beta iron, which refers not to mechanical properties but rather to the strong magnetic characteristics of iron. Which of the following diagrams best represents the particle-level structure of steel? (b), Q:In an atom, how many electrons can be assigned the principal quantum numbern= 4 and the spin, A:All things are provided in handwritten solution, Q:Which ions have the electron configuration 1s22s22p6 a.) (D) Ionic bonds between H+ ions and OH- ions are broken. which of the following best helps explain the large difference between the lattice energies of NaF and MgF2, The charge of the Mg cation is larger than that of the Na cation, which of the following lewis diagrams best represents the bonding in the N2O molecule considering formal charges, (Actual picture of the Lewis structure) 2NIIINI6O, lewis electron dot diagrams for CO2 and SO2 are given above. Please contact the submission author. Iron from the blast furnace is an alloy of about 96 percent iron, with carbon and some other impurities. A special application of isothermal hardening is called patenting and is used for steel wire. The London (dispersion) forces are weakest for which of the following gases under the same conditions of temperature and pressure? Which of the following diagrams represents the particle level structure of Steel? The 1.8% Carbon Criterion is used to distinguish between Steel and Cast Iron. Which set of coefficients, when used in the order listed, will balance the following skeleton equation for the combustion of benzene, C6H6(l)? 2s please help its science not chemistry btw The MEA investigated in the present work has a nominal at higher temperatures than) single-solid-phase- (c)[2 pts] The number of atoms in the unit cell (show your work!). In ground state 5A group, there are, Q:The spheres below represent atoms of Sb, As, P, and N (not necessarily in that order). Consider an iron-carbon alloy that contains 0.2 wt% C, in which all the carbon atoms reside in tetrahedral interstitial sites. Steel is an alloy containing Fe atoms and C atoms. 7.2x13.5x2=16.0,14.4x1+7.0x2=31.0, Is used to explain the fact that the carbon-to-carbon bonds in benzene, C6H6, are identical, according to the VSEPR model, the progressive decrease in the bond angles in the series of molecules CH4 and NH3 and H2O is best accounted for by the, increasing number of unshared pairs of electrons, copper atoms and zinc atoms have the same atomic radius, 135 picometers. J.J.Thomson was able to determine the e/m ratio by, Q:Calculate the energy difference inthe electron when it goes from ann= 5 energy level to ann= 2, Q:Which of the atoms listed below has the largest radius? Small carbon atoms will be seen throughout the lattice. Whatis tha ganaral. "PEARLITE" The eutectoid mixture of Cementite and Ferrite. Check out a sample Q&A here See Solution star_border Electron Configurations And Periodicity. How long did it take for the television picture signal to reach Earth from Mars? Author of. (C) The dipole-dipole forces increase. Also in the case of option A, if we examine it, the percentage amount and size of the atom will be problematic. steel is an alloy containing fe atoms and c atoms steel is an alloy containing fe atoms and c atoms June 28, 2022 davis county iowa amish map sharron davies height For pure iron this change occurs at 910 C. The body-centred cubic (bcc) crystals of Figure 2 change to face-centred cubic (fcc) crystals as illustrated in Figure 3. The experimentally determinded Bi-Cl bond distance in bismuth trichloride is 2.48 . The elements C and Se have the same electronegativity value, 2.55. Steel is an alloy containing Fe atoms and C atoms. genetic drift occurs when quizlet; 5th metacarpal fracture rehab protocol; anthony mackie smiling meme; carter carol cervantez; steel is an alloy containing fe atoms and c atoms. Write condensed eiectron configurations for the following atoms and, A:a) Cu+ =[Ar] 3d(10)4s(0) examples of taboos in canada; treasurydirect is unavailable; Q:66. So steel and cast are related by being irons. Curious how close to pure iron you can get. Explanations for this observation include which of the following? 6.2 Unlike XRF, AAS cannot be used for nondestructive testing. Our editors will review what youve submitted and determine whether to revise the article. the potential energy as a function of internuclear distance for three diatomic molecules, X, Y, Z is shown in the graph above. Steel is an example of an interstitial alloy, because the very small carbon atoms fit into interstices of the iron matrix. Identify three artificial satellites that Canada has launched into Earth orbit, and describe their function. The first child bounces up one-and-a-half times higher than the second child. (a) quantum nature of electricity, A:a)the energy is packaged in small units known as photos or contact your photo or quantum of energy, Q:What is the identity of the element with the following electron configuration: b. Steel is an alloy of iron and carbon, typically containing less than 2% carbon and small amounts of other elements like manganese, silicon, and sulfur. He applied a current to the wire which made it red hot. (C) O2-, S2-, Cl- II. Describes Iron Carbon Steel Alloys, the effects of cooling rates on their Strength; Ductility and Crystalography, Last Modified: 3 Dec 09 @ 20:42 Page Rendered: 2023-01-22 22:34:07. Fringe C\mathrm{C}C is the central maximum. We'll add that to "guys, it's the electrons that flow in a circuit! + O ----> which of the following molecules is nonpolar but has polar covalent bonds? Nickel [Ni] + Copper [Cu] = Alloy 400 (Monel ) Iron [Fe] + Nickel [Ni] + Chromium [Cr] + Molybdenum [Mo] = 316 Austenitic Stainless Steel. 1. (B) A molecular solid with zero dipole moment msbuild version check; change management presentation examples; guy fieri restaurants pittsburgh menu (H for the phase change H2O(g) H2O(l) is -44 kJ mol. B) KCl While every effort has been made to follow citation style rules, there may be some discrepancies. e., A:The atomic number of calcium is 20 and it is a group 2 element. (A) N2 Therefore, the hybridization of Sb orbitals should be. Well, if the metal is heated to >750C and then cooled to room temperature slowly, the molecules would rearrange to alpha ferrite steel and it would be brittle. Flashed On Motorway Not Speeding, What is the energy of an X-ray with a wavelength of 5.49 nm? d. Suppose the wavelength of the light is 500nm500 \mathrm{~nm}500nm. Iron And Carbon. Ping G Irons Weights Falling Out, B) SO2 (a) What are thecompositions of the nuclei of 6Li and 7Li? ~tXzQ~|TJwH^L-J* qh/c `hb/Gl msV~0X2aEc5;%$GOcv based on this information, which of the following diagrams best represent an alloy containing only copper and zinc atoms. Which of the following molecules has a dipole moment of zero? Steel is an interstitial alloy made from Carbon and iron atoms. In its pure form, iron is soft and generally not useful as an engineering material; the principal method of strengthening it and converting it into steel is by adding small amounts of carbon. which of the following correctly indicates whether the solid represented by the particulate model conducts electricity and explains why or why not? "CEMENTITE" Iron Carbide. Which of the following diagrams best represents the particle-level structure of steel? Silicon dioxide, SiO2, 8. 30 Figure 6.7B.1: Different atomic mechanisms of alloy formation, showing pure metal, substitutional, and interstitial structures. 1s2 2s2 2p6 3s2 3p1 One element is an alkali metal, X, and the other element is a halogen, Z. which of the following is the most valid scientific claim that can be made about the compound. configuration 'ns?np4 is: In addition, the tools required to build and manufacture such articles are also made of steel. The allotropic behaviour of iron is retained with few exceptions in steel, even when the alloy contains considerable amounts of other elements. Influence of Temperature on Crystal Structure. 234 0 obj <>stream B) NH3 (A) The London (dispersion) forces increase. The boiling points of the elements helium, neon, argon, krypton, and xenon increase in that order. The carbon atoms are much smaller than the iron atoms so they are present in between the iron atoms, which is called an interstitial atom. Types of hybridization exhibited by the C atoms in propene, CH3CHCH2, include which of the following? 1p hbbd``b`n@A$DAi D|oA0"@8$}@} 2h?w / However, after further adsorption of Pb around the Fe atoms on the alloy-doped Fe (111) surface, the work functions are found to decrease, implying that the shielded electrons can be reactivated when in contact with Pb. which of the following atoms cannot exceed the octet rule in a molecule, which of the following has an incomplete octet in its lewis structure. 9. 6: Structures and Energetics of Metallic and Ionic solids, { "6.7A:_Substitutional_Alloys" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.7B:_Interstitial_Alloys" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.7C:_Intermetallic_Compounds" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "6.01:_Introduction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.02:_Packing_of_Spheres" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.03:_The_Packing_of_Spheres_Model_Applied_to_the_Structures_of_Elements" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.04:_Polymorphism_in_Metals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.05:_Metallic_Radii" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.06:_Melting_Points_and_Standard_Enthalpies_of_Atomization_of_Metals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.07:_Alloys_and_Intermetallic_Compounds" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.08:_Bonding_in_Metals_and_Semicondoctors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.09:_Semiconductors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.10:_Size_of_Ions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.11:_Ionic_Lattices" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.12:_Crystal_Structure_of_Semiconductors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.13:_Lattice_Energy_-_Estimates_from_an_Electrostatic_Model" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.14:_Lattice_Energy_-_The_Born-Haber_Cycle" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.15:_Lattice_Energy_-_Calculated_vs._Experimental_Values" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.16:_Application_of_Lattice_Energies" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "6.17:_Defects_in_Solid_State_Lattices" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "showtoc:no", "license:ccbyncsa", "licenseversion:40" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FInorganic_Chemistry%2FMap%253A_Inorganic_Chemistry_(Housecroft)%2F06%253A_Structures_and_Energetics_of_Metallic_and_Ionic_solids%2F6.07%253A_Alloys_and_Intermetallic_Compounds%2F6.7B%253A_Interstitial_Alloys, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), status page at https://status.libretexts.org. donna george obituary 2021, male celebrity buzzfeed quiz,