Why do elements in a group have similar properties?
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OVERSIMPLIFIED ANSWER\n\nActually, the periodic table was a stunning predictor of properties of elements. When it was first formulated, many of the elements we know of today had not been discovered, and so it contained many blank spots. Interestingly enough, it turns out that the groupings predicted properties of elements in groups. For instance, you could be reasonably certain that if 12 new halogens are found in the future, they will all have similar properties to the halogens that are grouped together today.\n\nHow do we know this? How were the elements grouped by properties before we knew what those properties were? Simply put, the periodic table is organized like this\n\nRight to left: number of electrons in the outermost orbital\n\nTop to bottom: atomic weight\n\nThis is oversimplified, but it works here. Electron configuration in the outer orbital is what determines an element's reactivity, the bulk of its chemical properties. Since there are 8 rows from left to right in the table, elements read from top to bottom all have the same number of electrons in their outer orbitals, so they all have similar properties.\n\nWhat's important to remember is that much of the periodic table was organized in its modern state BEFORE we knew this. Pretty nifty.
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Yeah, there are some special cases with some transition metals, and you're right with groups 6 and 11.  \nYou'd expect for the Cu (and the other elements in that column) to have the electron configuration [Ar]4s2 3d9.  \nInstead, the configuration is [Ar]4s1 3d10.  This configuration is more stable because the d sublevel is completely filled.  Cr's valence electron configuration (and the rest of the column's) is expected to be 4s2 3d4, but it is actually 4s1 3d5.  There is added stability in the exactly half-filled d sublevel.
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Usually in an activity like this you are given clues as to the chemical and physical properties of each element.  the properties are the same, but the names are different. Use the clues given and what you can find out about the properties of the different families of elements to complete the activity.
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I would think your teacher is asking you about the way elements are grouped in the periodic table. You'll notice, for example, that gases are grouped together.\n\n Do a google on "classification of elements" -- there is a lot of stuff out there, and I'm sure it's also in your science text.
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Isomorphisms between groups are not the same thing as isomorphisms between, for example, rings.  There is a fully general definition of isomorphism that stems from universal algebra and mathematical logic, but I risk boring you if I develop it here.  So let me tackle the specific case of normed vector spaces, as I suspect it is in this setting that you came across the term "isometric isomorphism".\n\nTwo normed vector spaces are said to be isomorphic if there is a bijective map f between them that is homogeneous and linear, and for which there is a constant C>0 such that (1/C) ||x|| < ||f(x)|| < C ||x|| for all x.  An isometric isomorphism is an isomorphism for which that constant C can be taken to be 1, provided you reinterpret the symbol < as less than or equal--it's not easy to type the appropriate symbol.  In such a case, distances are not only roughly preserved (as in the case in which one has an isomorphism with constant C>1): they are indeed actually exactly preserved.  Thus the name isometry.
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i) x is an element of B (or a member of B)\nii) A is a subset of B \niii) C is a subset of D\niv) The set A has exactly 2,4, and 6 as members.
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Because there will always be interactions between all the elements in a compund except for a bridging ligand, we can asusme that we need to take into account the charge on each atom. \n\na element in group 2 is always +2\na element in group 4 is +2,3,4\nOxygen is is -2\n\nknowing we have a neutral charge we can immedialty eliminate C and as we know that we must use all of our atoms the only answer that makes sense is D
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It's called a unit element, because anything times 1\nequals itself.
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http://www.chemicool.com/definition/element.html\nis this what you mean? \n\nI don't think that this is a physical property although for the life of me I can't see why it couldn't be.
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The atomic radii for Cr, Mn, Fe, Co, Ni, and Cu are\n\nCr: 125 pm\nMn: 137 pm\nFe: 124 pm\nCo: 125 pm\nNi: 125 pm\nCu: 128 pm\n\nSo, you can see, there is a bit difference between their sizes. Although among them, Cr, Co, Ni, and Cu do have very similar atomic radius. \n\nThe reason that these elements have similar radius is due to their electron configurations. So, let's look at their corresponding electron configuration first (hope you know what I am referring to) :\n\nCr: [Ar] 3d5 4s1\nMn: [Ar] 3d5 4s2\nFe: [Ar] 3d6 4s2\nCo: [Ar] 3d7 4s2\nNi: [Ar] 3d8 4s2\nCu: [Ar] 3d10 4s1\n\nAs you may realize, the major difference between their electron configuration is mainly in the "3d" orbital, which has a quantum number (n) of 3; this 3d orbital has a smaller radius than the next orbital, 4s. The reason why 4s orbital is filled BEFORE 3d is due to the lower energy level of 4s compared to 3d.\n\nIn short, the major reason why these elements have similar radii is because the newly added electrons are not added to the "outermost electron shell", instead, they are added to the "inner electron shell". Therefore, no SIGNIFICANT changes to their radius.
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symetric properety...\n\n\nok heres why.....\n\n(pretend the equal signs are parallel line segments)\n\n===========================\n\n\ndo you see how you can split them dont the middle, thats called the symetric property
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well family 13 has B and Al.  they are metaloids that are great lewis acids.  they have interesting bonding strategies that defy the normal octet rule.
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A group, also known as a family, is a vertical column in the periodic table of the elements. \nGroups are considered the most important method of classifying the elements. In some groups, the elements have very similar properties and exhibit a clear trend in properties down the group — these groups tend to be given trivial (non-scientific) names, e.g. the alkali metals, alkaline earth metals, halogens and noble gases. \n\nSummary of Periodic Table Trends \n\nMoving Left --> Right \n\nAtomic Radius Decreases \nIonization Energy Increases \nElectronegativity Increases \nMoving Top --> Bottom \n\nAtomic Radius Increases \nIonization Energy Decreases \nElectronegativity Decreases \n\n\nThe Boron group is the series of elements in group 13 (IUPAC style) in the periodic table. These elements are characterized by having three electrons in their outer energy levels (valence layers). Boron is considered a metalloid, and the rest are considered metals of the poor metals group.\n\nThe boron group consists of boron (B), aluminium (Al), gallium (Ga), indium (In), thallium (Tl), and ununtrium (Uut) (unconfirmed).
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I'm assuming this is a group isomorphism. I will use "e_G" for the identity element of G, and "e_H" for the identity element of H.\n\nLet G and H be groups and f:G->H be an isomorphism. Let a be an element of G of infinite order. Suppose on the contrary that f(a) does not have infinite order. Then there exists some positive integer n such that e_H=f(a)^n=f(a^n), so a^n is in the kernel of f. Since f is an isomorphism, the kernel of f is {e_G}, thus it must be that a^n=e_G, contradicting that a has infinite order.
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G/H = {xH: x is in G}.\n\nAction: g.(xH) = (gx)H for every g and x in G.\n\nThis is indeed a left action because: (i) the group operation is associative (so (g''g').(xH) = g''.(g'.(xH)) for every g' and g'' in G and (ii) ex= x (so e.(xH) = xH).\n\nIt is transitive because, to satisfy g.(xH) = yH, it is enough to take g = y(x^-1)).\n\nNote: need H to be normal if the notation G/H is to be legit because it means the quotient group. H need not be normal for G to left-act on the *set* {xH: x is in G}, but this set won't be a group w/o normality of H.
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The representative elements are denoted with the last letter of "A" in the group names and there are eight major groups. Some of the more notable groupings are listed as follow: \n\nGroup IA (alkali metals) consists Li, Na, K, Rb, Cs, Fr \n\nGroup IIA (alkali earth metals) consists of Be, Mg, Ca, Sr, Ba, Ra. \n\nGroups IIIA, IVA, and VA elements are located close to the "staircase" that divides the metals on the left and the non-metals on the right. Most elements located along the "staircase" are classified as metalloids, e.g. B, Si, Ge, As, Sb, and Po. \n\nGroup VIA consists of O, S, Se, Te, and Po. \n\nGroup VIIA (halogens) consists of F, Cl, Br, I, and At. \n\nGroup VIIIA (rare gases) consists of He, Ne, Ar, Kr, Xe, and Rn.
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Assume that the numbers of elements of A1, A2, ..., An are m1, m2, ..., mn, respectively. Then their union has at most m1+m2+...+mn elements (exactly so many if the sets are disjoint, but if they have common elements then their union has less then m1+m2+...+mn elements), which is finite, because it is the sum of finitely many finite numbers.