K*p equation

Electronic states (with an appropriate choice of phases of the Bloch functions) near K and K points of two-dimensional (2D) graphite are described by the k p equation ... 

In the presence of lattice distortions, the k p equation is given by the 4x4 matrix equation given by... 

The generalised k p equation is the same as Eq.(5) except that the gap parameters are dependent on the position and should satisfy the boundary conditions ... 

The electrode process is a special case of the (Ag /Ag) couple, except that silver in the - -1 state collects as solid AgCI on the electrode itself. Even solid AgCl, however, has some Ag in equilibrium with it in solution. This [Ag" ] can be computed from the K p equation ... 

The activity of any solid is, by convention, unity. The equilibrium constant is thereby given in terms of the equilibrium concentrations of the dissolved ions and is referred to as the solubility product, or solubility constant, K p (equation 6.46). 

You now have both ion concentrations. Substitute into the K p equation and calculate the answer. 

Algebra is applied to find the solubility of ZnCOj. Let the letter s represent [Zn +] at equilibrium s = [Zn +]. Because [Zn +] = [COj "], s is also equal to [COj -]. Now substitute s for the two ion concentrations in the K p equation and calculate its value. (This will require using a procedure on your calculator that you have not performed in earlier problems in this book. The procedure is described in Appendix I.A.)... 

Upon doing so, the following set of equations is obtained (early referenees to the derivation of sueh equations inelude A. C. Wahl, J. Chem. Phys. 41,2600 (1964) and F. Grein and T. C. Chang, Chem. Phys. Lett. 12, 44 (1971) a more reeent overview is presented in R. Shepard, p 63, in Adv. in Chem. Phys. LXIX, K. P. Lawley, Ed., Wiley-Interseienee, New York (1987) the subjeet is also treated in the textbook Seeond Quantization Based Methods in Quantum Chemistry, P. Jorgensen and J. Simons, Aeademie Press, New York (1981))) ... 

Note that the brackets, [ ], refer to the concentration of the species. K,p is the solubility product constant hence [Cu " ] and [OH] are equal to the molar concentrations of copper and hydroxyl ions, respectively. The K p is commonly used in determining suitable precipitation reactions for removal of ionic species from solution. In the same example, the pH for removal of copper to any specified concentration can be determined by substituting the molar concentration into the following equation ... 

Electronic properties of CNTs, in particular, electronic states, optical spectra, lattice instabilities, and magnetic properties, have been discussed theoretically based on a k p scheme. The motion of electrons in CNTs is described by Weyl s equation for a massless neutrino, which turns into the Dirac equation for a massive electron in the presence of lattice distortions. This leads to interesting properties of CNTs in the presence of a magnetic field including various kinds of Aharonov-Bohm effects and field-induced lattice distortions. 

What conditions would be necessary for the apparent plate height to match the true plate height The first immediately obvious instance is when H, k and p are all constant. Then, the right-hand side of equation (7.5) reduces to H. If k and p were constant, or if the product (1-1- k)p were constant, then H would equal the spatial average of H. 

K value is the ratio of the cube root of a boiling temperature to gravity. There are two widely used methods to calculate the K factor K, and the K, p. The equations used for calculating both factors are as follows ... 

Furthermore, using the results of experiments done in acidified solutions, we can eliminate the methoxide ion terms and obtain the ratio k p/ksm directly. With that known, the preceding equation can be rearranged to the form... 

If the transfer constants k, p and p are known, then the hybrid transfer constants a and P are the roots of the quadratic equation ... 

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