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JEE Main 201911 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
11 January
Shift
Evening Shift
Subject
Chemistry
Chapter
Solid State

JEE Main 2019 · 11 January · Evening Shift · Chemistry · Solid State

The radius of the largest sphere which fits properly at the centre...

The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by 'a')

Options

  1. A0.027 a
  2. B0.047 a
  3. C0.134a0.134 \mathrm{a}
  4. D0.067 a

Correct answer

D. 0.067 a

Step-by-step solution

For bcc \Rightarrow R=3a4∴ Empty space at edge =\mathrm{R}=\frac{\sqrt{3} \mathrm{a}}{4} \therefore \text{ Empty space at edge }=a-2 R=a-3a2=\frac{\sqrt{3} a}{2}= diameter of sphere. \therefore \quad rsphere =a−32a2=(2−34)a=\mathrm{r}_{\text{sphere }}=\frac{a-\frac{\sqrt{3}}{2} \mathrm{a}}{2}=\left(\frac{2-\sqrt{3}}{4}\right) \mathrm{a}=0.067 a\mathrm{a}
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