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

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

best_answer

For an FCC, 4r=\sqrt{2}a

where r= radius of atom

a= edge length

\Delta 2d= \sqrt{2}a

\Delta 2d= \frac{\sqrt{2}a}{2}=\frac{\sqrt{2}}{2}\times 408

=204\sqrt{2}=288.456

\sim 288 pm


Option 1)

288 pm

This option is correct

Option 2)

408 pm

This option is incorrect

Option 3)

144 pm

This option is incorrect

Option 4)

204 pm

This option is incorrect

Posted by

Plabita

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