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: Calculate the Volume of the Atom
The volume \( V \) of a single atom (assuming it is spherical) can be calculated using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
Given that the radius \( r = 1.4 \) Å (which is \( 1.4 \times 10^{-8} \) cm), we can substitute this value into the formula.
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