The radius of an atom of gold (Au) is about 1.35 Å. c. If the atom is assumed to be a sphere, what is the volume in cm3 of a single Au atom?

Key Concepts

Atomic Radius

The atomic radius is a measure of the size of an atom, typically defined as the distance from the nucleus to the outermost electron shell. For gold (Au), the atomic radius is approximately 1.35 Å (angstroms), which is a unit of length equal to 10^-10 meters. Understanding atomic radius is crucial for calculating the volume of an atom, as it provides the necessary dimension for geometric calculations.

Volume of a Sphere

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. This formula is essential for determining the volume of a gold atom when it is approximated as a spherical shape. By substituting the atomic radius into this formula, one can find the volume in cubic centimeters (cm³), which is a standard unit for measuring volume.

Unit Conversion

Unit conversion is the process of converting a measurement from one unit to another. In this context, it is important to convert the volume calculated in cubic angstroms (ų) to cubic centimeters (cm³) for consistency with standard scientific measurements. Knowing the conversion factors, such as 1 Å = 10^-8 cm, allows for accurate and meaningful comparisons of atomic volumes.