Question

10. A drop of olive oil of radius 1mm spreads into a circular film of diameter 40 cm on water surface. Estimate the size of an oil molecule.

Answer 1

Volume of the drop-
$\frac43 \pi r^3$
= $\frac43 \pi (1 \times 10^{-3})^3$
= $\frac43 \pi \times 1 \times 10^{-9}$
= 4.2E-9 m cube
Surface area of the film-
$\pi r^2$
= $\pi (\frac{40}{2} \times 10^{-2})^2$
= 0.2E-2 m sq.

If we assume that the film is exactly one molecule thick, then,
diameter of an molecule= volume of the drop/surface area of the film
(Volume is constant)

diameter of an molecule= 4.2E-9/0.2E-2 = 21E-7 m = 2.1E-8 m = $2.1 \times 10^{-8}$ m

xEb = $x \times 10^b$