Question

1. Packing efficiency is the percentage of total space filled by the particles. Which of the following lattices has the highest packing efficiency? Simple cubic lattice, body centered cubic lattice, hexagonal close packed lattice.

2. An element has a body centred cubic structure with a cell edge of 288 pm. The density of the element is 7.2 g/cm³ . How many atoms are present in 208 g of the element?

Answer 1

1. Hexagonal close packed lattice.

2. a = 288 pm = 288 × 10^-10 cm

Volume of the unit cell = (288 × 10^-10cm)³

= 23.9 × 10^-24 cm³

Volume of 208 g of the element,

\(\frac{208g}{7.2gcm^{-3}}\) = 28.88 cm³

∴ Number of units cells in 208 g = \(\frac{28.88cm^3}{23.9\times10^{-24}cm^3}\)

= 1.208 × 10²⁴

For bcc structure, 

Number of atoms in one unit cell = 2

∴ Number of atoms in 208 g = 2 × 1.208 × 10²⁴

= 2.416 × 10²⁴