Question

Metal M crystallizes in BCC unit cell with edge length of 4 A°. calculate the density ( g/cc) of unit cell if polar mass of metal is 7 g/mol.
Taken Na = 6x 10^23

1. 0.131
2. 0.364
3. 7.3
4. 13.1

Answer 1

Given:

Edge length, a = 4 Angstrom

Molar mass, M = 7 gm/mol

Na = 6 × 10²³

To Find:

Density of the unit cell

Calculation:

- For BCC, z = 2

- Volume of unit cell, V = a³

⇒ V = (4 × 10⁻⁸)³ = 64 × 10⁻²⁴ cm³

- Using the formula:

V × Na × d = z × M

⇒ d = (z × M)/(V × Na)

⇒ d = (2 × 7)/( 64 × 10⁻²⁴ × 6 × 10²³)

⇒ d = 14/38.4

⇒ d = 0.364 gm/cm³

- So the correct answer is option (B) 0.364 gm/cm³.