91Ó°ÊÓ

The given data can be listed below as:

• Diameter of the copper atom is$\mathrm{d}=2.28×{10}^{-10}\mathrm{m}$
• Mass of one mole of copper is${\mathrm{m}}_1=64\mathrm{kg}×\left(\frac{{10}^{-3}\mathrm{kg}}{1\mathrm{g}}\right)=0.064\mathrm{kg}$
• The Avogadro’s number is$N=6.023×{10}^{23}$
• The side of the cube is, $l=4.6\mathrm{cm}×\left(\frac{{10}^{-3}\mathrm{m}}{1\mathrm{cm}}\right)=0.046\mathrm{cm}$$l=4.6\mathrm{cm}×\left(\frac{{10}^{-3}\mathrm{m}}{1\mathrm{cm}}\right)=0.046\mathrm{cm}$

The mass of one atom of an object is described as dividing the mass of one mole of that object and the Avogadro’s number. Moreover, the mass of a cubical block is expressed as the product of the number of atoms inside the cubical block and the mass of one atom.

The equation of the mass of one copper is expressed as:

$M=\frac{{\mathrm{m}}_1}{\mathrm{N}}$

Here, ${\mathit{m}}_{\mathbf{1}}$is the mass of one mole of copper and N is the Avogadro’s number.

Substitute all the values in the above equation.

$$\begin{gathered} M=\frac{0.064\mathrm{kg}}{6.023×{10}^{23}} \\ =1.06×{10}^{23}\mathrm{kg}/\mathrm{atom} \end{gathered}$$

Thus, the mass of one copper atom is $1.06×{10}^{-25}\mathrm{kg}/\mathrm{atom}$.

The equation of the number of the atoms in one cubical row is expressed as:

$$\begin{gathered} l=zd \\ z=\frac{l}{d} \end{gathered}$$

Here, l is the side of the cube, z is the number of atoms in one cubical row, and d is the diameter of the cube.

Substitute the values in the above equation.

role="math" localid="1656669222590" $$\begin{gathered} z=\frac{0.046\mathrm{m}}{2.28×{10}^{-10}\mathrm{m}} \\ =2.01×{10}^8 \end{gathered}$$

As the copper atom consists of three cubical blocks, hence the equation of the number of atoms in the cubical block is expressed as:

$a=z^3$

Here, a is the number of atoms in the cubical block and z is the number of atoms in one cubical row.

Substitute the value in the above equation.

role="math" localid="1656669407115" $$\begin{gathered} a={(2.01×{10}^8\mathrm{atom})}^3 \\ =8.12×{10}^{24}\mathrm{atom} \end{gathered}$$

Thus, the number of atoms in the cubical block is $8.12×{10}^{24}\mathrm{atom}$.

The equation of the mass of the copper cubical block is:

m = aM

Here, m is the mass of the copper cubical block, a is the number of atoms in the cubical block, and M is the mass of one copper atom.

Substitute the values in the above equation.

$$\begin{gathered} m=8.12×{10}^{24}\mathrm{atom}×1.06×{10}^{-25}\mathrm{kg}/\mathrm{atom} \\ =0.860\mathrm{kg} \end{gathered}$$

Thus, the total mass of the cubical block is 0.860 kg.