Find the simplest formula of a solid whose cubic unit cell has an 'x' atom at each corner, a 'y' atom at each face centre, and a 'z' atom at the body centre.

Options

A. `x_2yz`
B. `xy_2z`
C. `xy_3z`
D. `xyz_2`

Explanation

To find the simplest formula of a solid with a cubic unit cell containing 'x' atoms at each corner, 'y' atoms at each face center, and 'z' atoms at the body center, we can follow these steps:

### Step 1: Determine the contribution of corner atoms
In a cubic unit cell, there are 8 corners. Each corner atom is shared by 8 adjacent unit cells. Therefore, the contribution of the corner atoms to the unit cell is:
\[ \text{Contribution from corner atoms} = \frac{x \text{ atoms} \times 8 \text{ corners}}{8} = x \]

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