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One liter (1000 cm^3) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of 2 x 10^-10 m.

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My Work

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1. I will first change liters from cm^3 to m^3 so that the units will match up.

1 liter = 1000 cm^3 =1.0 x 10^-3 m^3

2. I will use the formula for volume of a cylinder (V = h π r^2) where:

V = 1.0 x 10^-3 m^3

h = 2 x 10^-10 m

r = unknown

3. Simply solve for the unknown radius:

(1.0 x 10^-3 m^3) = (2 x 10^-10 m) π r^2

(1.0 x 10^-3 m^3) / (2 x 10^-10 m) = π r^2

[(1.0 x 10^-3 m^3) / (2 x 10^-10 m)] / π = r^2

{[(1.0 x 10^-3 m^3) / (2 x 10^-10 m)] ^ (1/2)} =r = 1.3 x 10^3m

4. Calculate the diameter using the radius:

D = 2r

D = 2(1.3 x 10^3)

D = 2.5 x 10^3m

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Final Answer

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D = 2.5 x 10^3m

I have no idea if this is right or not, but it is as close as I have been able to get. This question has been giving me problems for hours. Can somebody confirm my calculation, or inform me where I went wrong?

Thanks,

Mitch

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# Homework Help: Simple problem. Please check my answer?

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