The determination of an atom diameter

A copper cube with a side length of 1 cm has a mass of $8.93$ g. The atoms are disposed as indicated. Calculate the diameter of one atom !

First calculate the number of moles of atoms in the cube !

Number of moles = $n$ $=$ $\frac{m}{M_{Cu}}$ $=$ $\frac{8,93}{63,55}$ $=$ $0.140$ mol

Then calculate the number of atoms in the cube

Number of atoms = $n\cdot6\cdot10^{23}$ $=$ $8.43\cdot10^{22}$ atoms

Then calculate the number of atoms on one ridge

Number of atoms on a ridge =$(8.43\cdot10^{22})^{\frac{1}{3}}$ $=$ $4.38\cdot10^7 $ atoms

Calculate a

$a$ $=$ $\frac{1}{4.38\cdot10^7}$ $=$ $2.28\cdot10^{-8}$ cm

$b^2$ $=$ $c^2$ $+$ $a^2$ $=$ $a^2$ $+$ $a^2$ $+$ $a^2$ (Pythagore), so $b$ $=$ $a\sqrt{3}$ $=$ $3.95\cdot10^{-8}$ cm

On the diagonal segment of the cube, the atoms are in contact, so you may calculate the diameter of one atom.

diameter =$\frac{b}{2}$ $=$ $1.98\cdot10^{-8}$ cm