A metal crystallizes with a face-centered cubic lattice. The edge of the unit cell is 408 pm. The diameter of the metal atom is:

  • Option 1)

    288 pm

  • Option 2)

    408 pm

  • Option 3)

    144 pm

  • Option 4)

    204 pm

 

Answers (1)

As we learnt in

No. of atoms(z) for face centered unit cell -

Lattice points: at corners and face centers of unit cell.

For face centered cubic (FCC), z=4.

- wherein

 

 

 

For an FCC lattices \sqrt{2}a=4r =2d

\Rightarrow d=\frac{a}{\sqrt{2}}=\frac{408}{\sqrt{2}}pm =288 pm

Correct option is 1.


Option 1)

288 pm

Correct

Option 2)

408 pm

Incorrect

Option 3)

144 pm

Incorrect

Option 4)

204 pm

Incorrect

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