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NEET 2012
Exam
NEET
Year
2012
Subject
Chemistry
Chapter
Solid State

NEET 2012 · Chemistry · Solid State

A metal crystallizes with a face-centered cubic lattice. The edge...

A metal crystallizes with a face-centered cubic lattice. The edge of the unit cell is 408pm408 \mathrm{pm}. The diameter of the metal atom is

Options

  1. A288pm288 \mathrm{pm}
  2. B408pm408 \mathrm{pm}
  3. C144pm144 \mathrm{pm}
  4. D204pm204 \mathrm{pm}

Correct answer

A. 288pm288 \mathrm{pm}

Step-by-step solution

For fcc lattice, 4r=2ar=24a=a22=40822=144pmdiameter d=2r=2×144pm=288pm\begin{aligned} & 4 r=\sqrt{2} a \\ & r=\frac{\sqrt{2}}{4} a=\frac{a}{2 \sqrt{2}} \\ & =\frac{408}{2 \sqrt{2}} \\ & =144 \mathrm{pm} \\ & \text{diameter } d=2 r=2 \times 144 \mathrm{pm} \\ & =288 \mathrm{pm} \end{aligned}
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