Suppose that F is the inverse square force field below, where c is a constant. F(r) = cr |r|3 r = x i + y j + zk

Required:
a. Find the work done by F in moving an object from a point P1 along a path to a point P2 in terms of the distances d1 and d2 from these points to the origin.
b. An example of an inverse square field is the gravitational field F = -(mMG)r/|r|3. Use part (a) to find the work done by the gravitational field

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.