Odd-numbered elements

Fig. 8.10. Odd-numbered element iron ratios measured in ultra-metal-deficient Galactic halo stars, after Cayrel et al. (2004).

It is also seen from Table 11.17 the crustal content of even-numbered elements is consistently higher than for odd-numbered elements. This observation is consistently higher than for the Oddo-Harkins rule according to which nuclei with equal numbers of protons and neutrons are inherently more stable than those which have an unpaired proton or neutron. 

Of the iron meteorites 99.22% of the material is made up of even nmn-bered elements, and of the stone meteorites, 97.50%. While the results for the earth s litho here are not so striking, they still show the same general tendency very strongly for, of the six most abundant elements, only aluminum is odd numbered, and the elements of even atomic number make up about 86% of the material. The only odd numbered elements other than hydrogen present in the lithosphere in amounts over 0.2% are aluminum, sodium, and potassium. 

If attention is now turned to the heavier elanents as shown in the model, it is seen that the five unknown elements eka-caesimn, e -manganese 1, eka-mmiganese 2 (dwi-manganese), eka-iodine, and eka-neodymium, have odd atomic numbers. (There is some doubt as to the discovery of thulium 2.) Not only are the unknown elements odd numbered, but among the radio-active elements, if the most stable isot( of each element is used for the comparison, the odd numbered elemente are much less stable than the adjacent elements of even number. 

The above results may be summarized by the statement that in the evolution of the elements much more material has gone into the even numbered elements than into those which are odd, either because the odd numbered elements are less stable, or because some constituent essential to their formation was not sufficiently abundant, or both. 

According to this interpretation, odd-numbered elements such as cobalt cannot form simple carbonyls M(CO), but they do form complex carbonyls, such as Co2(CO)s. These are solids, in contrast to the simple carbonyls, which are volatile liquids. 

In the lanthanide series the Marker rule—even-numbered elements are more abundant than odd-numbered elements—is well exemplified in the following abbreviated sequence for abundance (g/tonne) in igneous rocks atomic number 57 (lanthanum, 18.3),atomic number 58(cerium, 46.1), atomic number 59 (praseodymium, 5.5) [11]. 

What materials would be expected to exhibit paramagnetism Even-numbered elements will always have electrons in pairs hence, their magnetic moments will cancel each other. Odd-numbered elements, could have unpaired electrons, but generally this odd electron has formed either an ionic or covalent bond to form a full shell in which the electron pairs... 

Odd-numbered elements tend to have fewer isotopes than do even-numbered elements. Section 25-7 will explain why. 

For an isotropic material, all orientations are equally probable and all such products that have an odd number of Tike direction cosines will vanish upon averaging-. This restricts the nonvanishing tensor elements to those such as xVaaa abba - Similarly for the elements Such orientational averaging is crucial in... 

Because they possess an odd number of valence electrons the elements of this group can only satisfy the 18-electron rule in their carbonyls if M-M bonds are present. In accord with this, mononuclear carbonyls are not formed. Instead [M2(CO)s], [M4(CO)i2] and [M6(CO)i6] are the principal binary carbonyls of these elements. But reduction of [Co2(CO)g] with, for instance, sodium amalgam in benzene yields the monomeric and tetrahedral, 18-electron ion, [Co(CO)4] , acidification of which gives the pale yellow hydride, [HCo(CO)4]. Reductions employing Na metal in liquid NH3 yield the super-reduced [M(CO)3] (M = Co, Rh, Ir) containing these elements in their lowest formal oxidation state. 

The octet rule accounts for the valences of many of the elements and the structures of many compounds. Carbon, nitrogen, oxygen, and fluorine obey the octet rule rigorously, provided there are enough electrons to go around. However, some compounds have an odd number of electrons. In addition, an atom of phosphorus, sulfur, chlorine, or another nonmetal in Period 3 and subsequent periods can accommodate more than eight electrons in its valence shell. The following two sections show how to recognize exceptions to the octet rule. 

Nuclei with even numbers of both protons and neutrons are more stable than those with any other combination. Conversely, nuclei with odd numbers ot both protons and neutrons are the least stable (Fig. 17.12). Nuclei are more likely to be stable if they are built from certain numbers of either kind of nucleons. These numbers—namely, 2, 8, 20, 50, 82,114, 126, and 184—are called magic numbers. For example, there are ten stable isotopes of tin (Z = 50), the most of any element, but... 

When an element has an "odd" number of atoms on one side of the equation and an "even" number on the other side, it is often advisable to multiply the "odd" side by 2, then finish balancing. For example, if you have 3 carbon atoms on one side and 2 carbon atoms on the other, multiply the coefficients of the first side by 2 and the other side by 3. This way you ll have 6 carbons on both sides of the equation. 

All but one of the above structures have four helices in the bundle, with + 1,+ 1,+ 1 connections. For the up and down topology on a cylinder, handedness can be defined by whether the chain turns to the right or to the left at the end of the first structure element (whether it is a helix or a /3 strand). With an even number of helices, reversing N to C direction of the chain also reverses handedness of the topology for an odd number of helices or strands handedness is invariant to chain reversal. For + 1, + 1, +1 topologies in general, handedness is not... 

Restricting to the more common elements in organic mass spectrometry (H, B, C, N, O, Si, S, P, F, Cl, Br, I, etc.), a simple rule holds valid With the exception of N, all of the above elements having an odd number of valences also possess an odd mass number and those having an even number of valences have even mass numbers. This adds up to molecular masses fulfilling the nitrogen rule (Tab. 6.7). 

An odd property of many elements that helped scientists theoretically determine the characteristics of undiscovered elements is that elements having an even number of protons in their nuclei (atomic number) are more commonly found on Earth than are the elements with an odd number of protons. It is unclear why elements with odd numbers of protons in their nuclei are less commonly found than are those with even numbers of protons. 

Fig. 1.2 Number of stable isotopes of elements with even and odd number of protons (radioactive isotopes with half-lives greater than 10 years are included)...

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