Question

You can obtain a rough estimate of the size of a molecule by the following simple experiment. Let a droplet of oil spread out on a smooth surface of water. The resulting oil slick will be approximately one molecule thick. Given an oil droplet of mass 12.00 ✕ 10^-7 kg and density 878 kg/m³ that spreads out into a circle of radius 41.8 cm on the water surface, what is the order of magnitude of the diameter of an oil molecule?
1 m

Answer 1

The density of an object is its mass divided by its volume.Now the volume of oil in the droplet may be found from the equation, Volume = mass/density = (12 ✕ 10-7 kg)/(878 kg/m³) =13.667 x 10^-10 m³

The oil slick has a cylindrical shape with height h, equal to the diameter of an oil molecule and a circular cross-section of radius r=41.8 cm = 0.418 m.

Its volume is then given by,

Volume= Height x Cross-sectional area = h (pi * r²) = h *pi *(0.418)² =h(0.549) m²

Since the volume of the oil in the slick is the same as volume of the droplet,

  h(0.549) m² = 13.667 x 10^-10 m³

  From here h=2.489 x 10^-9 m

order of magnitude of diameter of oil molecule ~ 10^-9 m