A given metal crystallizes out with a cubic structure having edge length of 361 pm. If there are four metal atoms in one unit cell, what is the radius of one atom ?

  • Option 1)

    80 pm

  • Option 2)

    108 pm

  • Option 3)

    40 pm

  • Option 4)

    127 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

 

 Given that there are 4 metal atoms in a unit cell, so it's an FCC lattice.

4r=\sqrt{2}\:a

r=\frac{361}{2\sqrt{2}}=127pm

Answer is 4


Option 1)

80 pm

This solution is incorrect 

Option 2)

108 pm

This solution is incorrect 

Option 3)

40 pm

This solution is incorrect 

Option 4)

127 pm

This solution is correct 

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