A bcc lattic is made up of hollow spheres of X. spheres of soldid 'Y,' are present in hollow spheres of X. The radius of 'Y' is half of the radius of 'X' . Calculate the ratio of the total volume of spherees of 'X' unoccupied by Y in a unit cell and volume of the unit cell ?

Explanation

To solve the problem, we need to calculate the ratio of the total volume of spheres of 'X' unoccupied by 'Y' in a unit cell to the volume of the unit cell. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Geometry of the BCC Lattice
In a body-centered cubic (BCC) lattice, there are 2 effective atoms per unit cell. The atoms at the corners contribute 1/8th of their volume to the unit cell, and the atom at the center contributes fully.

### Step 2: Define the Radii
Let the radius of hollow sphere 'X' be \( R \). The radius of solid sphere 'Y' is given as half of that, so:
- Radius of \( Y = \frac{R}{2} \)
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