A crystal mth a simple cubic lattice and a monoatomic basis has an atomic ra- dius of 2.5 A and an atomic weight of 5.42. Calculate its density, assuming that the atoms touch each other.

density = 0.071984 g/cm³

Explanation:

For a simple cubic lattice structure;

There are 8 atoms in the unit cell, with each edge of the cell contributing 1/8th atom to one unit cell.

Thus, in a unit cell, the required number of atoms = 8/8 = 1

The mass of the unit cell can be calculated by using the formula:

Similarly, given the atomic radius = 2.5 angstrom =

Thus, volume V = a³

The edge length for the simple cubic radius  is:

a = 2 × r

a = 2 ×

a = m

a =

Now;

volume V = a³

volume V =

volume V = cm³

Finally; the density = mass/volume

density =  

density = 0.071984 g/cm³

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3