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Ch.2 - Atoms, Molecules, and Ions
All textbooksBrown 14th EditionCh.2 - Atoms, Molecules, and IonsProblem 19c
Chapter 2, Problem 19c

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?

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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.
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 meters into the volume formula.
Calculate the volume using the substituted values, ensuring that the units are consistent.
Express the final volume in cubic meters (m^3).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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Related Practice
Textbook Question
What fraction of the a particles in Rutherford's gold foil experimentare scattered at large angles? Assume the gold foilis two layers thick, as shown in Figure 2.9, and that the approximatediameters of a gold atom and its nucleus are 270pm and 1.0 * 10–2 pm, respectively. Hint: Calculate the crosssectional area occupied by the nucleus as a fraction of thatoccupied by the atom. Assume that the gold nuclei in eachlayer are offset from each other.
Textbook Question

Millikan determined the charge on the electron by studying the static charges on oil drops falling in an electric field (Figure 2.5). A student carried out this experiment using several oil drops for her measurements and calculated the charges on the drops. She obtained the following data: Droplet Calculated Charge (C) A 1.60 * 10-19 B 3.15 * 10-19 C 4.81 * 10-19 D 6.31 * 10-19 (b) What conclusion can the student draw from these data regarding the charge of the electron?

Textbook Question

Millikan determined the charge on the electron by studying the static charges on oil drops falling in an electric field (Figure 2.5). A student carried out this experiment using several oil drops for her measurements and calculated the charges on the drops. She obtained the following data: Droplet Calculated Charge (C) A 1.60 * 10-19 B 3.15 * 10-19 C 4.81 * 10-19 D 6.31 * 10-19 (c) What value (and to how many significant figures) should she report for the electronic charge?

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Textbook Question

The radius of an atom of copper (Cu) is about 140 pm. (a) Express this distance in angstroms 1A 2.

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Textbook Question

The radius of an atom of copper (Cu) is about 140 pm. (b) How many Cu atoms would have to be placed side by side to span a distance of 5.0 mm?

Textbook Question

The radius of an atom of copper (Cu) is about 140 pm. (c) If you assume that the Cu atom is a sphere, what is the volume in cm3 of a single atom?

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