Question

Find the packing efficiency of silver metal?

Answer 1

The packing efficiency of a metallic crystal is defined as the ratio of the volume occupied by the atoms in the unit cell to the total volume of the unit cell.

For face-centered cubic (FCC) metals like silver (Ag), the packing efficiency is given by:

Packing Efficiency:
\[ \text{packing efficiency} = \frac{4 \times (\text{volume of one atom})}{\text{volume of the unit cell}} \]

The volume of one atom is calculated using its atomic radius (144 pm for silver):

\[ \text{volume of one atom} = \frac{4}{3} \times \pi \times (144 \text{ pm})^3 = 2.52 \times 10^{-23} \text{ cm}^3 \]

The unit cell volume in an FCC lattice is:

\[ a = \frac{2 \times 144 \text{ pm}}{\sqrt{2}} = 408.3 \text{ pm} = 4.083 \times 10^{-8} \text{ cm} \]

\[ \text{volume of unit cell} = \frac{a^3}{4} = 6.21 \times 10^{-24} \text{ cm}^3 \]

Finally, the packing efficiency is:

\[ \text{packing efficiency} = \frac{4 \times 2.52 \times 10^{-23}}{6.21 \times 10^{-24}} = 0.74 \]

Thus, the packing efficiency of silver is approximately 74%.