Question

The planar density for (010) and (020) planes in simple cubic Polonium, which has a lattice parameter of 0.334 nm, is

• A. Packing density (010) = \(10.96 \times 10^{10} \, \text{atoms/cm}^2\), Planar packing fraction (020) = \(0 \, \text{atoms/cm}^2\)
• B. Packing density (010) = \(9.96 \times 10^{10} \, \text{atoms/cm}^2\), Planar packing fraction (020) = \(0 \, \text{atoms/cm}^2\)
• C. Packing density (010) = \(8.96 \times 10^{10} \, \text{atoms/cm}^2\), Planar packing fraction (020) = \(0 \, \text{atoms/cm}^2\)
• D. Packing density (010) = \(7.96 \times 10^{10} \, \text{atoms/cm}^2\), Planar packing fraction (020) = \(0 \, \text{atoms/cm}^2\)

Hint:

Planar density gives insights into how atoms are distributed across specific planes in a crystal. For simple cubic structures, low-index planes (e.g., (100), (010)) have atoms, but higher-index planes like (020) can be empty due to the lack of atomic presence. These properties affect material behavior such as cleavage and strength.

Answer 1

The Correct Option is C

In a simple cubic structure, packing density (PD) is defined as:
\[\text{Packing Density (PD)} = \frac{\text{Atoms per plane}}{\text{Area of the plane}}\]
For the (010) plane, the packing density is calculated as:
\[\text{PD} = \frac{1}{(0.334 \, \text{cm})^2} \approx 8.96 \times 10^{10} \, \text{atoms/cm}^2\]
For the (020) plane, the packing density is:
\[\text{PD} = 0 \, \text{atoms/cm}^2\]