Empirical Formula of CCP Unit Cell Compound

To determine the empirical formula of the chemical compound $\text{M}_p\text{X}_q$, we analyze the positions and contributions of each type of atom in the given unit cell:

1. Count and Contribution of $\text{M}$ Atoms (represented by squares $\square$):

• At 4 corners of the cubic unit cell: Each corner atom contributes $\frac{1}{8}$ to the unit cell. $\text{Contribution from corners} = 4 \times \frac{1}{8} = \frac{1}{2}$

• At 1 body center: The body-centered atom lies entirely inside the unit cell and contributes $1$. $\text{Contribution from body center} = 1 \times 1 = 1$

• Total number of $\text{M}$ atoms per unit cell ($N_{\text{M}}$): $N_{\text{M}} = \frac{1}{2} + 1 = 1.5 = \frac{3}{2}$

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2. Count and Contribution of $\text{X}$ Atoms (represented by circles $\bigcirc$):

• At all 6 face centers: Each face-centered atom contributes $\frac{1}{2}$ to the unit cell. $\text{Contribution from face centers} = 6 \times \frac{1}{2} = 3$

• Total number of $\text{X}$ atoms per unit cell ($N_{\text{X}}$): $N_{\text{X}} = 3$

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3. Empirical Formula Calculation:

The molar ratio of $\text{M}$ to $\text{X}$ in the unit cell is: $\text{Ratio } (\text{M} : \text{X}) = 1.5 : 3 = 1 : 2$

Thus, the empirical formula of the compound is $\text{MX}_2$.

Correct Option: (B)