Why does the law of conservation of energy limits the efficiency of any machine.

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 considering gravity acceleration and the force of acceleration, what must be true? a. the direction of acceleration must be perpendicular to the direction of the force. b. the direction of the force and the direction of acceleration must be the same as each other. c. the direction of the force and the direction of acceleration must be opposite of each other. d. the mass of the body must be the same as the acceleration of the body.

The charge on an electron is 1.60218 × 10−19 c and its mass is 9.10939 × 10−31 kg. how strong a magnetic field must be experienced by the electron if its path is a circle of radius 5.5 cm? answer in units of t.