The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are x: y : z. The numerical value of sum of x, y and z is _______ .

Options

A. `4 : 2 : 1 `
B. `8 : 1 : 6 `
C. `4 : 2 : 3 `
D. `1 : 2 : 4 `

Explanation

To solve the problem, we need to determine the number of atoms present in each type of cubic structure: Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). Then we will find the ratio of these numbers and calculate the sum.

### Step-by-Step Solution:

1. **Simple Cubic (SC) Structure:**
- In a simple cubic structure, there are 8 atoms located at the corners of the cube.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell because it is shared among 8 unit cells.
- Therefore, the total contribution from the corner atoms is:
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