Avalanche forecasters measure the temperature gradient startfraction dt over dh endfraction , which is the rate at which the temperature in a snowpack t changes with respect to its depth h. a large temperature gradient may lead to a weak layer in the snowpack. when these weak layers collapse, avalanches occur. avalanche forecasters use the rule of thumb that if startfraction dt over dh endfraction exceeds 10 degrees upper c divided by m anywhere in the snowpack, conditions are favorable for weak-layer formation, and the risk of avalanche increases. assume the temperature function is continuous and differentiable. complete parts (a) through (d) below. a. an avalanche forecaster digs a snow pit and takes two temperature measurements. at the surface (hequals0), the temperature is negative 12 degrees upper c. at a depth of 1.7 m, the temperature is negative 3 degrees upper c. using the mean value theorem, what can he conclude about the temperature gradient?

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.

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