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JEE Main 2006
Exam
JEE Main
Year
2006
Subject
Chemistry
Chapter
Solid State

JEE Main 2006 · Chemistry · Solid State

Total volume of atoms present in a face-centre cubic unit cell of a...

Total volume of atoms present in a face-centre cubic unit cell of a metal is ( rr is atomic radius)

Options

  1. A203πr3\frac{20}{3} \pi r^3
  2. B243πr3\frac{24}{3} \pi r^3
  3. C123πr3\frac{12}{3} \pi r^3
  4. D163πr3\frac{16}{3} \pi r^3

Correct answer

D. 163πr3\frac{16}{3} \pi r^3

Step-by-step solution

V=n×(43πr3)=4×(43πr3)=163πr3\begin{aligned} V & =n \times\left(\frac{4}{3} \pi r^3\right) \\ & =4 \times\left(\frac{4}{3} \pi r^3\right) \\ & =\frac{16}{3} \pi r^3\end{aligned}
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