The density of gold is 19 g/cm3. If 1.9×10−4 of gold is dispersed in one litre of water to give a sol having spherical gold particles of radius 10 nm, then the number of gold particles per mm3 of the sol will be

Volume of the gold dispersed in one litre water=MassDensity=1.9×10−4g19 g cm−3=1×10−5cm−3Radius of gold sol particle=10nm=10×10−9m=10×10−7cm=10−6cmVolume of the gold sol particle =43πr3=43×227×(10−6)3=4.19×10−18cm3No. of gold sol particle in 1×10−5cm3=1×10−54.19×10−18=2.38×1012No. of gold sol particle in one mm3=2.38×1012106=2.38×106