Question

Part C

Gallium crystallizes in a primitive cubic unit cell. The length of an edge of this cube is 362 pm. What is the radius of a gallium atom?

Express your answer numerically in picometers.

Part D

The face-centered gold crystal has an edge length of 407 pm. Based on the unit cell, calculate the density of gold.

Express your answer numerically in grams per cubic centimeter.

Answer 1

Concepts and reason

Crystal structure:

It is a systematic or periodic arrangement of atoms or ions in crystalline material. It is useful to predict properties of material.

Primitive Cubic Unit Cell:

In this unit cell, there are eight atoms those are arranged at the each corner of unit cell.

Face Centered Cubic (FCC):

In this unit cell, six atoms are presented in the center of six faces of unit cell. Another eight atoms are present in each corner of the unit cell.

Fundamentals

Density of the unit cell:

n = number of atoms per unit cell.

= density of unit cell.

A = atomic weight.

= volume per unit cell.

= Avogadro’s number.

Pythagoras's theorem:

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

(C)

In the primitive unit cell, the edge length (a) is equal to radius of the atom.

So,

(D)

The atomic weight of gold, A = 196.96654 g/mol.

Total number of atoms present in FCC unit cell = 4

The Avogadro’s number,

Ans: Part C

The radius of a gallium atom is 181 pm.

Part D

The density of gold is .