# Calculating the Radius of a Molecule

Assuming the molecule is a sphere, would the radius of amylopectin be $9.17*10^{-22}~cm^3$? I arrived at this answer by deriving the molar volume by dividing the molar mass ($828.72~g/mol$) of amylopectin by its density ($1.5~g/cm^3$). Then I divided the quotient by Avogadro's constant to arrive at my aforementioned answer. However, I don't know if this is correct so please correct me if I am not.

• The value you quote is a volume not a radius, so you need to take the cube root. Proteins are no more than a few nm ($10^{-9}$m) in radius. – porphyrin May 9 '18 at 17:01
• As @porphyrin pointed out, you got the volume of the particle, but should assume it as a cube instead of a sphere to avoid void volume trap among spheres on packing (see answer of TIME RUB below). Thus, the cube root of your answer gives you the length of a side of that cube. – Mathew Mahindaratne May 9 '18 at 18:29

When you divide the mass of the solid by its density then you get the volume of the object which means not only the volume of the molecules also the volume of voids. Now the volume you get is = volume of the particles + volume of voids. So the radius you get is = radius of void + radius of molecule. So in order to solve the problem you must which kind of packing is this. And then you should know it's packing efficiency. So now the volume you got should be multiplied by the packing efficiency to get the actual volume of molecules. If you say why do they have voids. Then I'll say you can't fill a particular shaped object with small sphere's so packing efficiency can't be 100%. So all you need to know is the kind of lattice formed by the molecules of amelopectin. And now what you got in your question is the volume of single particle + the volume of void. Well if you wanted to get the radius from it then it would be error as I said before. But in that case also you had to put $V=\frac{4}{3}\pi(r^3)$= the volume of the single molecule. And in this way you get the radius as 6.02*10^-8cm. And then get the radius. But actually taking the molecules as cube gives you a better answer though this would not give the proper answer if amilopectin molecules aren't cubic. But certainly you can fill a shape with cubes more efficiently (without having much voids) so in that case \$a^3=volume you mentioned which is 9.17*10^-22 cubic cm. That gives a as 9.7*10^-8cm as the side length.