According to legend, the following challenge led archimedes to the discovery of his famous principle: hieron, king of syracuse, was suspicious that a new crown that he had received from the royal goldsmith was not pure gold, as claimed. archimedes was ordered to determine whether the crown was in fact made of pure gold, with the condition that only a nondestructive test would be allowed. rather than answer the problem in the politically most expedient way (or perhaps extract a bribe from the goldsmith), archimedes thought about the problem scientifically. the legend relates that when archimedes stepped into his bath and caused it to overflow, he realized that he could answer the challenge by comparing the volume of water displaced by the crown with the volume of water displaced by an amount of pure gold equal in weight to the crown. if the crown was made of pure gold, the two volumes would be equal. if some other (less dense) metal had been substituted for some of the gold, then the crown would displace more water than the pure gold.

Complete the sentence to describe the law of conservation of energy. the law of conservation of energy states that energy cannot be created or , but it can be

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.

When the force acting on an object points at least partially in the direction of the motion the work done is considered to be negative