Consider a face-centered cubic monatomic bravais lattice in which each ion interacts only with its (twelve) nearest neighbors. assume that the interaction between a pair of neighboring ions is described by a pair potential depends only distance the pair of ions. show that the frequencies of the three normal modes with wave vector k are given by (a) a/m (22.960 where the are the eigenvalues of the 3 x 3 matrix: (22.97) here the sum is over the twelve nearest neighbors of r 0: (ty t z), (ti t r); (22.98) ow), and rr is the diadic formed from the unit vectors r r/r he, rr),v the constants a and b are: a 2g (d)/d, b 20p"(d) p'(d)/d], where

What happens when chlorine reacts with bromine? a. electrons move from the chlorine atoms to the bromine atoms. b. electrons move from the bromine atoms to the chlorine atoms. c. electrons are shared between the chlorine atoms and the bromine atoms. d. electrons become delocalized among the atoms.

The mass of a bowling ball is 10 kg and the mass of a ping pong ball is 0.015 kg. if the two objects are 5 meters apart, what is the gravitational force ?

Arunner is jogging at a steady 3.6 km/hr. when the runner is 2.9 km from the finish line, a bird begins flying from the runner to the finish line at 14.4 km/hr (4 times as fast as the runner). when the bird reaches the finish line, it turns around and flies back to the runner. even though the bird is a dodo, we will assume that it occupies only one point in space, i.e., a zero-length bird. how far does the bird travel? (b) after this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. the bird repeats the back and forth trips until the runner reaches the finish line. how far does the bird travel from the beginning? (i.e. include the distance traveled to the first encounter)