An atom of rhodium (Rh) has a diameter of about 2.7 ×10^-8 cm . (a) What is the radius of a rhod

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An atom of rhodium (Rh) has a diameter of about 2.7 ×10^-8...

An atom of rhodium (Rh) has a diameter of about $2.7 \times 10^{-8} \mathrm{cm} .$ (a) What is the radius of a rhodium atom in angstroms (A) and in meters $(\mathrm{m}) ?$ (b) How many Rh atoms would have to be placed side by side to span a distance of 6.0$\mu \mathrm{m}$ ? (c) If you assume that the Rh atom is a sphere, what is the volume in $\mathrm{m}^{3}$ of a single atom?

Key Concepts

Unit Conversion

This concept involves converting measurements between different units. It includes understanding the relationship between units such as centimeters, meters, angstroms, and micrometers. It is essential to know the conversion factors (e.g., 1 cm = 10^8 angstroms, 1 cm = 0.01 m, and 1 ?m = 10^-6 m) to accurately convert the dimensions of objects from one scale to another.

Relationship Between Diameter and Radius

This concept deals with the geometric relationship where the radius of a circle or sphere is half the length of its diameter. It is a fundamental principle that is widely used when transforming or calculating related properties such as surface area or volume.

Counting Discrete Units Over a Distance

This concept involves determining how many identical objects, each with a known dimension, are needed to span a given total length. It requires the application of division where the total length is divided by the individual dimension of an object, providing an estimate of the number of units in a linear arrangement.

Volume Calculation of a Sphere

This concept is about computing the volume of a spherical object using the geometric formula V = (4/3)?r³, where r is the radius. It is a key principle that connects the geometric shape to its volumetric properties and is widely applied in fields such as physics, chemistry, and material science to model atomic and molecular structures.

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