Consider a restricted 2d random walk the random on a square lattice with lattice constant a walker is not allowed to step back, but it ca go forward, turn right and turn left with can 1 equal probability. calculate the mean-square end-to-end distance for such a restricted n-step random walk starting with the general equation n n 2(cos (0)) r2) (3) = a i=1 j=1 which in this case can be evaluated analytically. note that the values for the cosines can be only 0, 1 or - on the square lattice. derive the exact result for the characteristic ratio cn.

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

Sound is a disturbance that travels through a medium as a

Alandscaper is shopping for landscaping materials. she wants to use materials through which water flows easily. which materials should she choose? check all that apply. clay gravel granite rocks with cracks loosely packed soil