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

One gram of a water insoluble substance of density 0.8 g cm^(-3) is de

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