A bcc lattice is made up of hollow spheres of X. Spheres of solid '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 spheres of 'X' unoccupied by Y in a unit cell and volume of the unit cell ?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define the radius of spheres
Let the radius of the hollow spheres of X be denoted as \( r \). According to the problem, the radius of the solid spheres of Y is half that of X, which can be expressed as:
\[ r_Y = \frac{r}{2} \]

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