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?

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Convert the radius from angstroms to centimeters. Recall that 1 Å = 1 \(\times\) 10^{-10} meters and 1 meter = 100 cm.

Use the formula for the volume of a sphere, which is V = \(\frac{4}{3}\) \(\pi\) r^3, where r is the radius of the sphere.

Substitute the radius in centimeters into the volume formula.

Calculate the value inside the formula without rounding off too early to maintain accuracy.

Express the final volume of the gold atom in cubic centimeters (cm^3).

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주요 개념

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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 (Å³) 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.