Question

Silver crystallizes in a face-centered cubic lattice. The lattice parameter of silver (in picometer) is .............

Hint:

For FCC structures: convert cm → pm carefully (1 cm = 10$^{10}$ pm).

Answer 1

Correct Answer: 408

Step 1: Use density formula for cubic crystals.
\[ \rho = \frac{Z M}{a^3 N_A} \] For FCC: Z = 4 atoms/unit cell.
Given: density = 10.5 g/cm$^3$,
atomic mass = 107.87 g/mol.
Step 2: Rearranging the density formula.
\[ a^3 = \frac{4 \times 107.87}{10.5 \times 6.023 \times 10^{23}} \] Calculate numerically: \[ a^3 = 6.82 \times 10^{-23} \text{ cm}^3 \] Step 3: Cube root.
\[ a = (6.82 \times 10^{-23})^{1/3} = 4.09 \times 10^{-8}\text{ cm} \] Step 4: Convert to picometers.
\[ 4.09 \times 10^{-8} \text{ cm} = 409 \text{ pm} \] Step 5: Conclusion.
Thus, the lattice parameter of FCC silver is 409 pm.