P9E.11 (a) For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2p orbital, the energies E, of the resulting A molecular orbitals are given by: E, =a+2B cos- N+1 k=1, 2,.,N Use this expression to make a reasonable empirical estimate of the resonance integral B for the homologous series consisting of ethene, butadiene, hexatriene, and octatetraene given that t-n ultraviolet absorptions from the HOMO to the LUMO occur at 61 500, 46 080, 39 750, and 32 900 cm", respectively. (b) Calculate the T-electron delocalization energy, Egdo:= E, - n(a+ B), of octatetraene, where E, is the total T-electron binding energy and n is the total number of T-electrons. (c) In the context of this Hückel model, the molecular orbitals are written as linear combinations of the carbon 2p orbitals. The coefficient of the jth atomic orbital in the kth molecular orbital is given by: cN sin j=1,2.N jkn j=1, 2,.,N Evaluate the coefficients of each of the six 2p orbitals in each of the six T molecular orbitals of hexatriene. Match each set of coefficients (that is, each molecular orbital) with a value of the energy calculated with the expression given in part (a) of the molecular orbital. Comment on trends that relate the energy of a molecular orbital with its shape, which can be inferred from the magnitudes and signs of the coefficients in the linear combination that describes the molecular orbital.

Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum energy must be added to the molecule to dissociate it-that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule. For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13×10−10m and the dissociation energy is 1.54×10−18J per molecule. Find the value of the constant a. Find the value of the constant b.

What are the most common elemental dopants in the solar cell industry to create n+ -type and p-type regions, respectively? Please schematically illustrate their doping mechanisms based on atomic lattices.

Below is the LCAO for the sp3 hybrid orbital. What is the value for the c²? (The answer mus be a number, not a fraction) Ya = C($25 +02p₂ +$2p, + $2p:) 2Px

Consider n-doped Ge with N=10¹8 cm-³ with mobility 300 cm²/Vs at room temperature T=300 K. Calculate approximate thermoelectric transport coefficients: 1) mean free path, 2) resistivity, 3) Seebeck coefficient, 4) Peltier coefficient, and 5) electronic thermal conductivity. Use materials parameters for the effective density of states in the conduction band N=10¹⁹ cm³³.

Solve as soon as possible

A K* and a CI- ion are separated by 0.52 nm. Find the Coulomb component of the binding energy at that distance. Give your answer in electron-volts. (Please include the appropriate sign.) A positive binding energy would mean the ions are unbound and a negative binding energy means they are bound. Note: For this homework problem, round your answer to 2 decimal places.

a) Explain how the alpha parameter in the general E(p) relation, and the channel dimension could be used to determine the density of states as function of the energy E.        b) Provide and define the two main parameters (terms) that determine the electron density when temperature is non zero.

H5

Clear my CHOICE A laser beam with a power of 200 mW and frequency v= 15 x 1014 Hz is incident on a Si photo-detector doped with Na = 1 x 1012 cm3 fully ionized with an absorption coefficient as = 1 x 10 cm1. At steady state and assuming the electrons and holes recombination life times are T = To = 1 ns. Based on that calculate the total concentration of holes (p) in the valence band. Select one: OA. P = 2.01e12 /cm^3 OB. P = 2.25e15 /cm^3 • C.P = 2.25e16 /cm^3 OD. P = 2.25e18 /cm^3 OE. P = 2.25e17 /cm^3 Clear my choice ol muantum efficiency (the radiative recombination efficiency) n