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Solid State question

2016 · Shift 2 · Q4
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Solid State question

2016 · Shift 2 · Q4

JEE AdvancedChemistrySolid StateMultiple correct+4 / −2
The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are) :
  1. A
    The number of the nearest neighbours of an atom present in the topmost layer is 12
  2. B
    The efficiency of an atom packing is 74%
  3. C
    The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively
  4. D
    The unit cell edge length is 222 \sqrt 222​ times the radius of the atom
View written solutionFree

Correct answer: C, B, D

  1. Identify the structure

Cubic close packing (ccp) is the same as face-centered cubic (fcc) packing.

For ccp/fcc:

  • Coordination number of a bulk atom =12=12=12
  • Packing efficiency =74%=74\%=74%
  • Number of octahedral voids per atom =1=1=1
  • Number of tetrahedral voids per atom =2=2=2
  • Edge length relation: a=22 ra = 2\sqrt{2}\,ra=22​r

  1. Check each option

Option A:

"The number of the nearest neighbours of an atom present in the topmost layer is 12"

This statement is not correct as written.

In a ccp structure, an atom in the bulk has coordination number 121212. But an atom in the topmost layer is on the surface, so it does not have all 12 nearest neighbours because atoms are missing above it.

Hence, A is incorrect.


Option B:

"The efficiency of an atom packing is 74%"

For ccp/fcc packing, Packing efficiency=74%\text{Packing efficiency} = 74\%Packing efficiency=74%

Hence, B is correct.


Option C:

"The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively"

In ccp/fcc packing:

  • octahedral voids per atom =1=1=1
  • tetrahedral voids per atom =2=2=2

Hence, C is correct.


Option D:

"The unit cell edge length is } 2\sqrt 2 \text{ times the radius of the atom"

For fcc, atoms touch along the face diagonal.

Face diagonal =a2= a\sqrt{2}=a2​

Along one face diagonal, there are four radii: a2=4ra\sqrt{2} = 4ra2​=4r a=4r2=22 ra = \frac{4r}{\sqrt{2}} = 2\sqrt{2}\,ra=2​4r​=22​r

Hence, D is correct.


  1. Final derived answer

Correct statements are: B, C, D\boxed{B,\ C,\ D}B, C, D​


  1. Comparison with stored correct answer

Stored correct answer: C, B, D

This matches my derived answer exactly (order does not matter).

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