A metal (`M^(@) = 100` gm/mole) having density 10 gm/`cm^(3)` forms a cubic lattice. If radius of an atom is 1.4 Å find packing fraction. `[N_(A)=6xx10^(23)` perm ole].

Options

A. `0.74`
B. `0.69`
C. `0.52`
D. `0.90`

Explanation

To find the packing fraction of the metal, we will follow these steps:

### Step 1: Determine the number of atoms per unit cell (Z)
For a simple cubic lattice, there is 1 atom per unit cell. This is because there are 8 corners in a cube, and each corner atom is shared by 8 unit cells. Therefore, the contribution from the corners is:
\[ Z = 8 \times \frac{1}{8} = 1 \]

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