Consider the eigenvalue problemφ′′(x) +λφ= 0. Determine the eigenvaluesλandthe corresponding eigenfunctionsφifφsatisfies the following boundary conditions. Consider all three casesλ= 0,λ >0 andλ <0 and assume that the eigenvalues are real.

Using the work energy theorem. what is the velocity of a 850kg car after starting at rest when 13,000j of work is done to it.

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.

Suppose while hauling rocks, you accidentally drop one. it breaks apart in flat, planar sections. what type of rock did you just drop? 20 points