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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?

Respuesta :

Answer:

Time will be equal to 0.0208 sec

Explanation:

We have given that bacterium with radius greater than [tex]10\mu m=10^{-6}m[/tex]

So [tex]x_{rms}=10^{-6}m[/tex]

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

We have to find time t

We know that [tex]x_{rms}[/tex] is given by

[tex]x_{rms}=\sqrt{6Dt}[/tex]

So [tex]10^{-6}=\sqrt{6\times 8\times 10^{-10}\times t}[/tex]

[tex]10^{-12}={6\times 8\times 10^{-10}\times t}[/tex]

[tex]t=0.0208sec[/tex]

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