Question

An element crystallizes in a bcc lattice of edge length 4 \AA. If the density of the element is 10 g cm\(^{-3}\), what is its atomic weight (g mol\(^{-1}\))?

• A. 96
• B. 124
• C. 192
• D. 235

Hint:

For cubic crystals use \(\rho = \frac{Z M}{N_A a^3}\) and always convert Å to cm.

Answer 1

The Correct Option is C

Step 1: Density formula for a cubic lattice.
ρ = (Z × M)/(N_A × a³), where Z = 2 for bcc.

Step 2: Unit conversion of edge length.
a = 4 Å = 4 × 10⁻⁸ cm, so a³ = 64 × 10⁻²⁴ cm³.

Step 3: Plugging in the values.
10 = (2 × M)/(6.022×10²³ × 64×10⁻²⁴).

Step 4: Simplifying the denominator.
6.022×10²³ × 6.4×10⁻²³ ≈ 38.53.

Step 5: Determining M.
10 = (2M)/38.53 → M = (10×38.53)/2 ≈ 192 g mol⁻¹.

Step 6: Conclusion.
The molar mass of the element is approximately 192 g mol⁻¹.