Atomic radius of BCC structure is given by ______.

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  1. \(\frac{{a\sqrt 3 }}{4}\)
  2. \(\frac{{4a}}{{\sqrt 3 }}\)
  3. \(\frac{a}{{2\sqrt 2 }}\)
  4. \(a{\rm{ }}/{\rm{ }}2\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{{a\sqrt 3 }}{4}\)

Detailed Solution

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Explanation

BCC crystal structure: BCC stands for Body-Centered Cubic. In one unit cell, there is one atom at center, 1 atom at each corner. The crystal structure is used for Brittle materials only. 

F1 Ashik Madhu 14.08.20 D27

AC = Body diagonal of the unit cell

a = Side of the unit cell

\(a√ 3 = 4r\)

\(r = \frac{{√ 3 a}}{4}\)

26 June 1

characteristics

BCC

FCC

HCP

a to r relation

\(a = \frac{{4r}}{{√ 3 }}\)

 

a=2r√2 

\(a = 2r\)

The average number of atoms

2

4

6

Co-ordination number

8

12

12

APF

0.68

0.74

0.74

Examples

Na, K, V, Mo, Ta, W

Ca, Ni, Cu, Ag, Pt, Au, Pb, Al

Be, Mg, Zn, Cd, Te

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