Question

An element crystallizes in the body-centered cubic unit cell. It has a molar mass of 120.4 g/mol and an atomic radius of 1.45 × 10^(-8) cm. What is the density of the element?

a) 2.43 g/cm³
b) 4.86 g/cm³
c) 6.12 g/cm³
d) 8.14 g/cm³

Answer 1

The density of an element can be calculated using its molar mass and atomic radius. The formula for density is mass divided by volume. In this case, the element crystallizes in a body-centered cubic unit cell.

Step-by-step explanation:

The density of an element can be calculated using its molar mass and atomic radius. The formula for density is mass divided by volume. In this case, the volume is the volume of the unit cell.

The molar mass of the element is given as 120.4 g/mol. The atomic radius is given as 1.45 × 10^(-8) cm. To calculate the volume of the unit cell, we can use the formula: volume = (√3/4) * a^3, where a is the edge length of the unit cell.

Given that the element crystallizes in a body-centered cubic unit cell, the edge length is equal to 4 * atomic radius / √3. Substituting the given atomic radius, we can calculate the edge length and then the volume.

Finally, we can calculate the density using the formula: density = mass / volume. Substituting the given molar mass and the calculated volume, we can find the density of the element.

The correct answer is (c) 6.12 g/cm³.