Question

The size of spherical aerobic bacteria is limited by the rate at which oxygen diffuses through water. A bacterium with a radius greater than roughly 10 μm is not able to obtain enough oxygen from the surrounding water to sustain itself. Given that the diffusion constant of oxygen in water is 8 ×10−10 m2s-1, how long does it take oxygen in water to diffuse an RMS distance of 10 μm?

Answer 1

Answer:

Time will be equal to 0.0208 sec

Explanation:

We have given that bacterium with radius greater than $10\mu m=10^{-6}m$

So $x_{rms}=10^{-6}m$

Diffusion constant $D=8\times 10^{-10}m^2/sec$

We have to find time t

We know that $x_{rms}$ is given by

$x_{rms}=\sqrt{6Dt}$

So $10^{-6}=\sqrt{6\times 8\times 10^{-10}\times t}$

$10^{-12}={6\times 8\times 10^{-10}\times t}$

$t=0.0208sec$