Question

If in a certain material whose atoms are in a cubic array the interatomic distance is $\mathbf{1}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}\mathbf{}\mathbf{m}$and the mass of one atom is $\mathbf{8}\mathbf{.}\mathbf{26}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{26}}\mathbf{}\mathbf{kg}$, what be the density of this material?

Short answer

The density of the material is $1.7\times {10}^4\mathrm{kg}/{\mathrm{m}}^3$.

Step-by-step solution

Identification of given data

The given data is listed as follows,

• Interatomic distance of the atom is,$a=1.7\times {10}^{-10}\mathrm{m}$
• The atom’s mass is, $M=8.26\times {10}^{-26}\mathrm{kg}$

Significance of the density

The density of the material is referred to as the ratio of mass to volume. Moreover, density is also described as the degree of the compactness of a particular substance.

Calculation of the density

The density of an atom is calculated by:

$d=\frac{M}{V}$ …(i)

Here, $M$is the mass of the atom, and $V$is the Volume.

Also$V=a^3$

Substitute all the values in equation (i).

$$\begin{gathered} d=\frac{M}{a^3} \\ =\frac{8.2\times {10}^{-26}\mathrm{kg}}{\left(1.7\times {10}^{-10}\mathrm{m}\right)} \\ =1.7\times {10}^4\mathrm{kg}/{\mathrm{m}}^3 \end{gathered}$$

Thus, the density of the material is $1.7\times {10}^4\mathrm{kg}/{\mathrm{m}}^3$.