(c) Using the volume of a silver atom and the formula for the volume of a sphere, calculate the radius in angstroms of a silver atom.

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insert step 1> Determine the volume of a silver atom. This information might be given directly in the problem or you may need to calculate it using the density and molar mass of silver.

insert step 2> Recall the formula for the volume of a sphere: $V = \frac{4}{3} \pi r^3$, where $V$ is the volume and $r$ is the radius.

insert step 3> Rearrange the formula to solve for the radius $r$: $r = \left(\frac{3V}{4\pi}\right)^{1/3}$.

insert step 4> Substitute the volume of the silver atom into the rearranged formula to calculate the radius.

insert step 5> Convert the radius from meters to angstroms, knowing that 1 angstrom = \$10^{-10}$ meters.

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Key Concepts

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

Volume of a Sphere

The volume of a sphere is calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius. This formula is essential for determining the size of spherical objects, such as atoms, by relating their volume to their radius. Understanding this relationship allows for the conversion of volume measurements into linear dimensions.

Atomic Volume

Atomic volume refers to the space occupied by a single atom, typically expressed in cubic centimeters or cubic angstroms. For silver, this value can be derived from its molar volume and density. Knowing the atomic volume is crucial for calculating the radius of an atom, as it provides the necessary information to apply the volume formula effectively.

Unit Conversion to Angstroms

An angstrom (Å) is a unit of length equal to 10^-10 meters, commonly used in chemistry to express atomic and molecular dimensions. When calculating the radius of an atom, it is important to ensure that all measurements are in consistent units. Converting the radius from centimeters or other units to angstroms allows for easier comparison and understanding of atomic sizes.

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Textbook Question

In 2009, a team from Northwestern University and Western Washington University reported the preparation of a new 'spongy' material composed of nickel, molybdenum, and sulfur that excels at removing mercury from water. The density of this new material is 0.20 g/cm³, and its surface area is 1242 m² per gram of material. (b) Calculate the surface area for a 10.0-mg sample of this material.

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Textbook Question

U.S. 1-cent coin (a penny) has a diameter of 19 mm and athickness of 1.5 mm. Assume the coin is made of pure copper,whose density and approximate market price are 8.9 g/cm3and \$2.40 per pound, respectively. Calculate the value ofthe copper in the coin, assuming its thickness is uniform.

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