Question

A certain metal M crystallizes in a lattice described by a face-centered cubic (fcc) unit cell. The radius r of M atoms has been measured to be 179.pm. Calculate the lattice constant a of a crystal of M. Be sure your answer has the correct number of significant digits, and be sure it has the correct unit symbol.

Answer 1

Answer: The lattice constant 'a' of the crystal of M is 506. pm

Explanation:

We are given:

Atomic radius of metal M = 179 pm

To calculate the edge length, we use the relation between the radius and edge length for FCC lattice:

$a=2\sqrt{2}R$

Putting values in above equation, we get:

$a=2\sqrt{2}\times 179=506.3pm$

Hence, the lattice constant 'a' of the crystal of M is 506. pm