Circumference of a Sphere Formula

From left to right across the four blocks of the long- or 32-column form of the periodic table are a series of linking or bridging groups of elements, located approximately between each block.[49] These groups, like the metalloids, show properties in between, or that are a mixture of, groups to either side. Chemically, the group 3 elements, scandium, yttrium, lanthanum and actinium behave largely like the alkaline earth metals[50] or, more generally, s block metals[51][52] but have some of the physical properties of d block transition metals.[53]Lutetium and lawrencium, at the end of the end of the f block, may constitute another linking or bridging group. Lutetium behaves chemically as a

lanthanide but shows a mix of lanthanide and transition metal physical properties.[54][55] Lawrencium, as an analogue of lutetium, would presumable display like characteristics.[n 6] The coinage metals in group 11 (copper, silver, and gold) are chemically capable of acting as either transition metals or main group metals.[58] The volatile group 12 metals, zinc, cadmium and mercury are sometimes regarded as linking the d block to the p block. Notionally they are d block elements but they have few transition metal properties and are more like their p block neighbors in group 13.[59][60] The relatively inert noble gases, in group 18, bridge the most reactive groups of elements in the periodic table—the halogens in group 17 and the alkali metals in group 1.

In 1789, Antoine Lavoisier published a list of 33 chemical elements, grouping them into gases, metals, nonmetals, and earths.[61] Chemists spent the following century searching for a more precise classification scheme. In 1829, Johann Wolfgang Döbereiner observed that many of the elements could be grouped into triads based on their chemical properties. Lithium, sodium, and potassium, for example, were grouped together in a triad as soft, reactive metals. Döbereiner also observed that, when arranged by atomic weight, the second member of each triad was roughly the average of the first

and the third;[62] this became known as the Law of Triads.[63]German chemist Leopold Gmelin worked with this system, and by 1843 he had identified ten triads, three groups of four, and one group of five. Jean-Baptiste Dumas published work in 1857 describing relationships between various groups of metals. Although various chemists were able to identify relationships between small groups of elements, they had yet to build one scheme that encompassed them all.[62]

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