Question

Certain metal crystallizes in cubic order with centers in the body and with unit cell edge length of 3,147 Å. Determine its density.

Answer 1

To determine the density of a metal with a cubic crystal structure, you need to know the atomic radius and the edge length of its unit cell. The atomic radius can be calculated using the relation: radius = edge length / 2√3. The density can then be calculated using the formula: density = 4 * molar mass / (number of atoms * edge length).

Step-by-step explanation:

To find the density of a metal with a cubic crystal structure, we need to know its atomic radius and the edge length of its unit cell. The atomic radius can be found by using the relation: radius = edge length / 2√3.

The density can then be calculated using the formula: density = 4 * molar mass / (number of atoms * edge length^3), where the number of atoms is determined by the crystal structure.

For example, for tungsten:

1. Using the given unit cell edge length of 3.165 Å, the atomic radius can be calculated as 1.58 Å.
2. Using the molar mass of tungsten (183.84 g/mol) and the calculated atomic radius and edge length, the density can be calculated as 19.25 g/cm³.

Similarly, for platinum:

1. The edge length of the cubic closely packed structure is equal to the diameter of one atom, which is twice the atomic radius. Thus, the edge length can be calculated as 2 * 1.38 Å = 2.76 Å.
2. Using the molar mass of platinum (195.08 g/mol) and the calculated edge length, the density can be calculated as 21.46 g/cm³.