Estimating oil molecule diameter

Bolter · Dec 21, 2019

Can anyone help me in what assumptions I can make and how to justify them for when working out diameter of the molecule in part b) of this question? You can see the method that I have used in my workings but how would I explain it in words?

I obtained the diameter to be 0.13 nano metres which seems like a sensible length for a molecules diameter?

Exam question sheet with part (a) on a steel wire of diameter 6.00 mm and length 4.00 m supporting a 15.0 kg mass, with sub-parts i to iii and marks, and part (b) on estimating the diameter of an oil molecule from an oil drop spreading on water to a 400 mm patch.

Handwritten working on lined paper showing stress equals F over A, stress = 4mg over pi d squared, strain calculations giving 2.7 x 10^-5, extension L = 1.06 x 10^-4 m, and energy E = half Fx giving approximately 8 mJ.

Handwritten working for oil drop diameter estimate: sketch of a flat oil patch cylinder of radius r and thickness d, drop volume V = (1/6)πd^3 = 6.54 x 10^-11 m^3, and d = 6.54 x 10^-11 / (π(0.4)^2) = 1.3 x 10^-10 m = 0.13 nm.

Thanks for any help! :)

gneill · Dec 21, 2019

How did you arrive at the radius of the cylinder being 0.4 (presumably meters)?

Handwritten calculation of d = 6.54 x 10^-11 / (pi r^2), then 6.54 x 10^-11 / (pi (0.8 - 1)^2) = 13 x 10^-10 m = 0.13 nm, with the term (0.8 - 1)^2 circled in red.

Bolter · Dec 22, 2019

gneill said:

How did you arrive at the radius of the cylinder being 0.4 (presumably meters)?

View attachment 254528

I made a silly mistake and used the diameter's length in metres and not the radius length. So it should have read 0.2m instead.

I have changed from 0.4 to 0.2 and get the thickness of d to be 0.521 nano metres now

Handwritten derivation of oil film thickness: a sketch of a thin disc of radius r with thickness d, volume of a sphere-shaped drop equated to a cylinder volume, giving d = 6.54 x 10^-11 / (pi r^2) = 0.521 nm.

gneill · Dec 22, 2019

Yes, that looks better!

Bolter · Dec 22, 2019

gneill said:

Yes, that looks better!

Ok so the only assumption that I have made in this problem is that the cylinder thickness is 1 molecule's diameter thick. How do I justify such an assumption?

gneill · Dec 22, 2019

Bolter said:

Ok so the only assumption that I have made in this problem is that the cylinder thickness is 1 molecule's diameter thick. How do I justify such an assumption?

Perhaps look into surface tension.

Bolter · Dec 22, 2019

gneill said:

Perhaps look into surface tension.

Possibly.
I think I'll need to look into that more myself before I make my own justification as I'm a bit hazy over that. But thank you :)

Estimating oil molecule diameter

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