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Calculate the lattice parameter of chromium assuming tight atomic bonding.

  • A.1.442 Å
  • B.2.880 Å
  • C.4.323 Å
  • D.5.764 Å

Answer: B

The lattice parameter is 2.880 Å.

In bcc the atoms touch along the body diagonal, which spans four atomic radii, or two diameters:

\[ \begin{aligned} \sqrt{3}\,a &= 4r = 2d \\ a &= \frac{2(2.494)}{\sqrt{3}} = 2.880\ \text{Å} \end{aligned} \]

1.442 Å is half of that, using the radius where the diameter belongs. 4.323 Å and 5.764 Å come from the wrong geometry, for example treating the face diagonal or the cube edge as the touching direction.

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