Question

10 The fraction of the total volume occupied by the atoms present in a simple cube is a) π/4 b)π/6 c)π/3√2 d)4√2​

Answer 1

$\bigstar \underline{\underline{\sf \bf To\ Find:-}}$

• The fraction of the total volume occupied by the atoms present in a simple cube.

$\bigstar \underline{\underline{\sf \bf Solution:-}}$

Let a = edge length of cube.

Then,

$\\ \\ :\implies \sf Radius = \frac{a}{2}$

For a simple cube ,

No of atom/unit cell (z) :

$\\\\ :\implies \sf Z =8\times \frac{1}{8} \\\\:\implies \sf \bold{Z=1.}$

The packing fraction :-

$\\\\ \mapsto \boxed{\boxed{\sf Packing\ fraction=\frac{z \times \frac{1}{4} \pi r^3}{a^3}}}$

Where,

=> a = edge length

=> r = radius

$:\implies \sf \frac{(1)\times \frac{4}{3} \pi (\frac{a}{2})^3 }{a^3}\\\\\\:\implies \sf \pink{\boxed{\frac{\pi }{6} }}$

Hence, Option(B) is correct.

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HOPE IT HELPS !