The radius of an atom of tungsten (W) is about 2.10 Å. (c) If the atom is assumed to be a sphere, what is the volume in m³ of a single W atom?

Verified step by step guidance

1. Convert the radius from angstroms to meters. Since 1 angstrom (A) is equal to 1 x 10^{-10} meters, multiply the radius by this conversion factor.
2. 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.
3. Substitute the radius in meters into the volume formula.
4. Calculate the volume using the substituted values, ensuring that the units are consistent.
5. Express the final volume in cubic meters (m^3).

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 outer boundary of the surrounding cloud of electrons. For tungsten (W), the atomic radius is approximately 2.10 angstroms (A), which is a unit of length equal to 10^-10 meters. Understanding atomic radius is essential for calculating the volume of an atom, as it provides the necessary dimensions 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 crucial for determining the volume of a tungsten atom when it is approximated as a spherical shape. By substituting the atomic radius into this formula, one can find the volume in cubic meters, which is necessary for understanding the spatial properties of the atom.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this context, it is important to convert the atomic radius from angstroms to meters to ensure consistency in the volume calculation. Since 1 angstrom equals 10^-10 meters, proper unit conversion is essential for accurately calculating the volume of the tungsten atom in cubic meters.