Vanadium crystallizes in a body-centered cubic lattice, and the length of the edge of a unit cell is 305 pm. What is the density of V A) 5.96 * 10^-30 g/cm³ B) 2.98 * 10^-6 g/cm³ C) 2.98 g/cm³ D) 5.96 g/cm³ E) 11.9 g/cm³

Question

Quizplus · Accepted Answer

To find the density of V, we first need to determine its atomic mass. From the periodic table, the atomic mass of V is 50.94 g/mol.

Next, we need to determine the number of atoms present in one unit cell of V. In a body-centered cubic lattice, there are two atoms per unit cell - one at each corner of the cell and one at the center of the cell. Therefore, the number of atoms in one unit cell of V is 2.

The volume of one unit cell can be calculated using the formula: V = a^3, where a is the length of the edge of the unit cell. Substituting the given value of a, we get:

V = (305 pm)^3 = 2.99 x 10^-23 cm^3

Now, we can calculate the density of V:
density = mass/volume
mass = Number of atoms x Atomic mass
mass = 2 x 50.94 g/mol = 101.88 g

density = 101.88 g / 2.99 x 10^-23 cm^3
density = 3.411 x 10^22 g/cm^3
density = 5.96 g/cm^3 (rounded to two significant figures)

Therefore, the answer is D.

Vanadium Crystallizes in a Body-Centered Cubic Lattice, and the Length