If the edge length of a unit cell is 200 pm (200 × 10⁻¹² m), the unit cell's volume is calculated as (200 × 10⁻¹² m)³ = 8 × 10⁻³⁰ m³. For a face-centered cubic (fcc) structure, the number of atoms per unit cell (n) is 4. The mass of the unit cell is determined as n × A = 4 × 200 / 24 × 10²

Question

If the edge length of a unit cell is 200 pm (200 × 10⁻¹² m), the unit cell's volume is calculated as (200 × 10⁻¹² m)³ = 8 × 10⁻³⁰ m³. For a face-centered cubic (fcc) structure, the number of atoms per unit cell (n) is 4. The mass of the unit cell is determined as n × A = 4 × 200 / 24 × 10²³ = 33.3 × 10⁻²³ g. Using the formula density = mass of unit cell / volume of unit cell, what is the density of the unit cell in g cm⁻³?

Accepted Answer

41.6 g cm⁻³. Volume = 8e-30 m^3 = 8e-24 cm^3, and mass = 33.3e-23 g. Density = (33.3e-23)/(8e-24) = 41.6 g/cm^3, so the correct option is 41.6 g/cm^3.

Solution

Related JEE Advanced Chemistry questions