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2. Suppose we model a bacterium as a sphere of radius R in a lake. The oxygen concentration in the water far from the bacterium is constant [i.e. c(r=infinity) equals c?]. The bacterium gobbles up the oxygen at its surface such that c(r=R) equals 0. Under this condition, the oxygen concentration around the bacterium c(r) does not change with time. We derived an expression for c(r) in class and showed that there is a maximum rate of oxygen uptake defined by ‘I’, the number of oxygen molecules that diffuse through the water and are consumed by the bacterium per second. Assume the diffusion constant for O? is D=10?? m²/s. a) Determine ‘I’ in molecules/ second when R = 1 µm and c?=0.2 mole/m³ b) Metabolic activity of an organism is given by (I/ m) : the rate of oxygen consumption divided by its mass. The mass density of the bacterium can be assumed to be the same as that of water (1000 kg/ m³). Find out the maximum possible metabolic activity of a spherical bacterium as a function of the radius R of the bacterium. c) The actual metabolic activity of a certain bacterium is ~ 0.001 mole kg?¹s?¹ . Using the expression found in (b), what is the maximum possible radius of this bacterium?

          2. Suppose we model a bacterium as a sphere of radius R in a lake. The oxygen concentration in the water far from the bacterium is constant [i.e. c(r=infinity) equals c?]. The bacterium gobbles up the oxygen at its surface such that c(r=R) equals 0. Under this condition, the oxygen concentration around the bacterium c(r) does not change with time. We derived an expression for c(r) in class and showed that there is a maximum rate of oxygen uptake defined by ‘I’, the number of oxygen molecules that diffuse through the water and are consumed by the bacterium per second. Assume the diffusion constant for O? is D=10?? m²/s.
a) Determine ‘I’ in molecules/ second when R = 1 µm and c?=0.2 mole/m³
b) Metabolic activity of an organism is given by (I/ m) : the rate of oxygen consumption divided by its mass. The mass density of the bacterium can be assumed to be the same as that of water (1000 kg/ m³). Find out the maximum possible metabolic activity of a spherical bacterium as a function of the radius R of the bacterium.
c) The actual metabolic activity of a certain bacterium is ~ 0.001 mole kg?¹s?¹ . Using the expression found in (b), what is the maximum possible radius of this bacterium?

2. Suppose we model a bacterium as a sphere of radius R in a lake. The oxygen concentration in the water far from the bacterium is constant [i.e. c(r=infinity) equals c?]. The bacterium gobbles up the oxygen at its surface such that c(r=R) equals 0. Under this condition, the oxygen concentration around the bacterium c(r) does not change with time. We derived an expression for c(r) in class and showed that there is a maximum rate of oxygen uptake defined by ‘I’, the number of oxygen molecules that diffuse through the water and are consumed by the bacterium per second. Assume the diffusion constant for O? is D=10?? m²/s.
a) Determine ‘I’ in molecules/ second when R = 1 µm and c?=0.2 mole/m³
b) Metabolic activity of an organism is given by (I/ m) : the rate of oxygen consumption divided by its mass. The mass density of the bacterium can be assumed to be the same as that of water (1000 kg/ m³). Find out the maximum possible metabolic activity of a spherical bacterium as a function of the radius R of the bacterium.
c) The actual metabolic activity of a certain bacterium is 0.001 mole kg?¹s?¹ . Using the expression found in (b), what is the maximum possible radius of this bacterium?

Added by Kara L.

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