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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Convert the radius from picometers to centimeters. Since 1 pm = 1 x 10^{-12} m and 1 m = 100 cm, multiply the radius by 1 x 10^{-12} and then by 100 to convert to cm.

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

Substitute the converted radius into the volume formula.

Calculate the cube of the radius.

Multiply the result by \(\frac{4}{3}\) \(\pi\) to find the volume in cm^3.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Atomic Volume Calculation

To calculate the volume of a spherical atom, we use the formula for the volume of a sphere, V = (4/3)πr³, where r is the radius. In this case, the radius of the copper atom is given in picometers (pm), which must be converted to centimeters (cm) for the final volume calculation.

Unit Conversion

Unit conversion is essential in chemistry to ensure that measurements are in compatible units. Since the radius of the copper atom is provided in picometers, it must be converted to centimeters (1 pm = 1 x 10^-10 cm) before using it in volume calculations to maintain consistency in units.

Spherical Geometry

Understanding the geometry of a sphere is crucial for this problem. A sphere is defined as a three-dimensional shape where all points on the surface are equidistant from the center. This geometric property is fundamental when applying the volume formula, as it directly relates to how we perceive the size and space occupied by an atom.