SATHEE: The Solid State - Result Question 24

The Solid State - Result Question 24

####24. The fraction of total volume occupied by the atoms present in a simple cube is

[2007]

(a) $\frac{π}{3 \sqrt{2}}$

(b) $\frac{π}{4 \sqrt{2}}$

(d) $\frac{π}{6}$

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Solution:

(d) Number of atoms per unit cell $= 1$

Atoms touch each other along edges. Hence $r = \frac{a}{2}$

( $r =$ radius of atom and $a =$ edge length)

Therefore fraction $= \frac{\frac{4}{3} π r^{3}}{(2 r)^{3}} = \frac{π}{6} = 0.52$

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The Solid State - Result Question 24

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