Question

A given metal crystallizes out with a cubic structure having an edge length of 360 pm. If there is only one metal atom per unit cell, what is the radius of the atom?​

Answer 1

Given: cubic structure having an edge length of 360 pm

         one metal atom per unit cell

To Find: radius of the atom

Explanation:

If there is only one metal atom per unit cell, then the cell is Simple cubic cell.

For simple cubic cell, $\frac{1}{8} \times 8=1 cell$

In this type of crystal lattice, the boundaries of two adjacent atoms touch each other.

$a = 2r$

where a= edge length = 360 pm

r= radius of the atom

$a = 2r\\360 = 2r\\\frac{360}{2} = r\\180 = r$

Hence, the radius of the atom that crystallizes out in simple cubic cell is 180 pm.