Suppose we have a cube of `1.00 cm` length. It is cut in all three directions, so as to produce eight cubes, each `0.50 cm` on edge length. Then suppose these `0.50` cm cubes are each subdivided into eight cubes `0.25` cm on edge length, and so on. How many of these successive subdivisions are required before the cubes are reduced in size to colloidal dimensions of `100 nm`.

Explanation

We find that every division in two equal halves also reduces the size of edge lengths to one half.
In first subdivision `1` cm is reduceds to `0.5 cm=1/2 cm`.
In second subdivision `0.5 cm` is reduced to `0.25 cm =1/4 cm =(1/2)^(2) cm`
In n subdivision `1` cm is reduced to `(1/2)^(n)`. Size of colloidal particles lies between `1` to `1000 mm`. Thus to make n subdivision required particle size may be attained.
`(1/2)^(n)=100 nm =100xx10^(-9) m =100xx10^(-7) cm`
`:. n log 2=5`
`nxx0.3010=5`
`n=5/0.3010=16.61=17` subdivision are required for dimension of `100 nm`.