One gram of a water insoluble substance of density `0.8 g cm^(-3)` is dispersed in 1 L of water forming a colloidal solution having `10^13` particles of spherical shape per `mm^3`. Calculate the radius of the particle.

Explanation

Particles present in `1 mm ^(3)` of the solution `=10^(13)`
`therefore` Paticles present in `1 cm^(3)` of the solution `=10^(13)xx10^(3)=10^(16)`
Particles present in `1 L (1000cm^(3))` of the solution `=10^(16)xx10^(3)=10^(19)`
Mass of the substance dispersed =1 g
Density of the substance `=0.8 g cm^(-3)`
`therefore` Volume of the dispersed substance `=(1.0)/(8.0)=1.25cm^(3)`
`therefore` Volume of 1 particle `=(1.25)/(10^(19))=1.25xx10^(19)cm^(3)`
But volume `=4/3pi r^(3)=1.25xx10^(19)cm^(3)`
or `r^(3)=3/4xx7/22xx1.25xx10^(-19)=29.8xx10^(-21)cm^(3)`
`r=(29.8)^(1//3)xx10^(-7)cm=3.1xx10^(-7)cm=310xx10^(-9)m=310 nm`