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What is the n...

Question

What is the number of atoms in a cube based unit cell having one atom on each corner and two atoms on each diagonal?

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Solution

$N o . o f c o r n e r s = 8 c o n t r i b u t i o n o f 1 c o r n e r s = \frac{1}{8} T o t a l c o n t r i b u t i o n f r o m 8 c o r n e r s = \frac{1}{8} \times 8 = 1 a t o m N o . o f d i a g o n a l s = 4 c o n t r i b u t i o n o f 1 d i a g o n a l s = 2 (g i v e n) T o t a l c o n t r i b u t i o n f r o m 4 d i a g o n a l = 4 \times 2 = 8 a t o m T o t a l n o . o f a t o m = 8 + 1 = 9 a t o m$

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