Dot and cross

Alternatively, the electron can exchange parallel momentum with the lattice, but only in well defined amounts given by vectors that belong to the reciprocal lattice of the surface. That is, the vector is a linear combination of two reciprocal lattice vectors a and b, with integer coefficients. Thus, g = ha + kb, with arbitrary integers h and k (note that all the vectors a,b, a, b and g are parallel to the surface). The reciprocal lattice vectors a and are related to tire direct-space lattice vectors a and b through the following non-transparent definitions, which also use a vector n that is perpendicular to the surface plane, as well as vectorial dot and cross products ... 

Fig. 7.15 The contributions to the normalized heats of formation, AH/(AN)2, for the case of 4d transition metal alloys. The experimental and semi-empirical values of Miedema eta/. (1980) for A/V = 1 and 2 are given by the solid dots and crosses respectively. (From Pettifor (1987).)...

Figure 6. Results of applying the LUT algorithm to synthetic extinction spectra calculated from measured pre- and post-Pinatubo size distributions obtained from Pueschel el al. [9], Goodman el al [10] and Deshler el al. [11,12]. R,/bimodal) is the effective radius of the measured bimodal size distribution, and R /uni modal) is the corresponding effective radius returned by the LUT. The dots are results obtained when a range of distribution widths are considered in the LUT calculations and the crosses are results obtained when at is restricted to the value that yields the best fit between calculated and measured extinction spectra. The solid and dashed curves are second order polynomial fits to the dots and crosses, respectively.

Alkanes and alkenes are hydrocarbons. They are composed of molecules which contain covalent bonds. For each of the molecules below, use a dot and cross diagram to show the bonding it contains, a Methane, CH4. 

A Draw dot and cross diagrams to represent electrons to show how you would expect atoms for the following elements to combine, what ions would be produced, and what the formulae of the resulting compounds would be. 

This type of diagram is usually called a dot and cross diagram because the electrons from the different atoms are shovm as dots and crosses (although, of course, there is no real difference between the electrons of different atoms). 

Draw dot and cross diagrams to show the electron distribution in the following ... 

It would be rather inconvenient to have to draw a dot and cross diagram every time to describe the bonding in molecules, so a kind of shorthand is used. We simply use a line joining the two atoms to represent a shared pair of electrons or single covalent bond. The line represents one electron from each atom. 

The element to the left of nitrogen is carbon. This has four electrons in its valence shell in the uncharged atomic state. Thus, in order to achieve the octet it must combine with four other atoms, and so form four single covalent bonds. Draw the dot and cross structure of the tetrahydride of carbon, i.e. methane. 

There is one more carbon species that is encountered less frequently. Propose an equation for the production of the species that results from the loss of the XT anion from the CX3 species. Draw its dot and cross structure. 

Draw a dot and cross structure for the diatomic molecule of nitrogen. 

In the molecule diimide, HN=NH, there is a double nitrogen/nitrogen bond. Draw the dot and cross structure for this molecule. 

Carbon may form double or triple bonds with itself. Draw a dot and cross representation for these species, namely R2C=CR2 and R-C=C-R Note the symbol R is used to indicate a general alkyl... 

Carbon may also form multiple bonds with many other elements. It is this ability that is one of the reasons for the richness of the chemistry of carbon. One of the commonest heteroatomic multiple bond systems in which carbon partakes involves oxygen. Draw the dot and cross structure of this carbon/ oxygen double bond system. 

Draw a dot and cross representation of the cyanide group. Then suggest the direction of polarisation, if any, along this bond system. 

Draw the dot and cross structure of the imine group, 1 0= and again suggest the direction of... 

Now that the three-dimensional structure of the molecule is important, the dot and cross notation, which was so useful when counting electrons around each atom, is of less utility. First, it is rather cumbersome and secondly, it does not... 

The value of the dot and cross structure here is to help to ensure that all the electrons are accounted for before attempting to deduce the structure. The electron pair repulsion theory gives the result that the CC12 molecule has a trigonal planar shape. There are two C-Cl single bonds and also (formally)... 

There is another, rather unusual, functional group that is related to the cyanide group. It contains a carbon atom that is only doubly bonded to a nitrogen atom, but which is not involved in any further bonding. This is the isocyano group, RNC. Draw the dot and cross structure of this grouping. 

The simplest, commonly encountered, charged hydrocarbon species is the methyl cation, CH3+. Draw a dot and cross structure of this ion, and suggest a shape for it. 

In a carbon centre that is involved in four covalent single bonds, how many electrons are there around the carbon atom Demonstrate your answer by focusing on the carbon atom in a molecule of methane, CH4, and drawing a dot and cross structure for it. 

Carbon has four electrons in its valence shell and needs four more electrons to reach the stable octet of electrons. It may do this by combining with four hydrogen atoms to form a methane molecule. Write down a dot and cross representation of this molecule and calculate the charge that is present on each of the five atoms. 

Draw the dot and cross representation of the dihydride of oxygen, i.e. water, and so calculate the charge that is resident on each of the three atoms. 

Write the equation that represents the further addition of another hydrogen cation to the hydroxonium ion. Draw a dot and cross structure for the resultant ion. 

If you are having problems, try to write a balanced equation for the formation of this species from known species, and then try to draw the dot and cross structure. 

---