Consider a spherical gold nanoparticle that is 3 nm in diame

Consider a spherical gold nanoparticle that is 3 nm in diameter. If the diameter of an atom is approximately 3 A?, how many atoms are on the surface of the particle? What fraction of the gold atoms in the particle are on the surface?

Solution

number of partical on surface is given by
4pie 3nm^2 =n*4pie3A^2

hence n =100

spherical nanopartical hence total no of atoms =n*4/3 pie *3A^3 =4/3 *pie*3nm^3

n\' =1000

....

hence fraction is n/n\' =100/1000 =0.1