e) The amount of energy the worm needs from its metabolism should be proportional to the worm'svolume. What is the ratio of the metabolic needs of the larger warm compared to the smallerworm? Why might the metabolic need limit the increase in thickness of these flatworms?f) If the oxygen diffusion coefficient in the worm body is 1.4 x 105 cm² /s, how long does it takeoxygen to diffuse to the center of the worm if its total thickness is 1mm?g) Diffusion times can be long, as long as there is a steady supply of oxygen for the worm’smetabolic needs. Scientists have measured the oxygen metabolic rate, m, for a number of wormsand used that to determine the maximum thickness of a worm. This thickness will also depend onthe concentration difference driving oxygen diffusion. The maximum diffusion rate occurs whenthe concentration inside the worm goes to 0 (all the oxygen is used up). Since the concentrationdifference driving diffusion is Cocean - Cworm, the maximum concentration difference is just Cocean.Based on all that, the maximum worm thickness is given bymax thickness2DC,mOceanWe'll assume the diffusion coefficient is the same as in part f and the oxygen concentration in theocean is 2.7 x 104 mol /1. Scientists have measured worm metabolic rates as 100 microliters ofoxygen / gram of worm / hr. This is equivalent to 1.2 x 106 moles /1/ sec. What is the maximumworm thickness? Quantitative: Fick's first law helps us understand the relationshipbetween a molecule's concentration gradient (the difference in itsconcentration at two locations) and diffusive flux. In organismswithout circulatory systems, the delivery of oxygen to their bodytissues can be limited by diffusion. Therefore, diffusion canliterally determine the allowable thickness of their body. Oneexample of an organism like this is a flatworm. There are over30,000 species of marine flatworms which are often beautifullycolored. Let's think more about what might be happening in aflatworm's body.a) Draw a picture of a slice through a flatworm showing its cross section and the water above andbelow. We'll let the total worm thickness be 2Ax which will simplify things as we go.b) Write Fick's equation for the flux of oxygen from the water above into the center of the worm.Label your drawing above with the key variables in this equation.c) A typical marine flatworm is about 1 mm thick. If the worm's thickness were to double, whatwould happen to the oxygen flux to the worm's center?d) Now assume that the worm gets bigger in all three dimensions, doubling in length, width andthickness. We'll also assume that oxygen diffuses into the worm primarily across its large surfacearea determined by the length and width (essentially ignoring the tiny area from the thin edgesaround the worm). What is the ratio of the oxygen diffusion rate for the larger worm compared tothe smaller worm?

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e) The amount of energy the worm needs from its metabolism should be proportional to the worm's volume. What is the ratio of the metabolic needs of the larger warm compared to the smaller worm? Why might the metabolic need limit the increase in thickness of these flatworms?