Calculate the approximate wavenumber and wavelength of the fundamental absorption due to the stretching vibration of a carbonyl group C=O. the force constant for the typical double is 1x 10³ N/m.

H1.

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…

5.47 Germanium is doped with 5 × 10¹5 donor atoms per cm³ at T = 300 K. The dimen- sions of the Hall device are d = 5 x 10-³ cm, W = 2 × 10-² cm, and L = 10-¹ cm. The current is I = 250 μA, the applied voltage is V. = 100 mV, and the magnetic flux density is B₂ = 500 gauss = 5 x 10-2 tesla. Calculate: (a) the Hall voltage, (b) the Hall field, and (c) the carrier mobility.