Carbon-12 contains 6 protons and 6 neutrons. The radius of...

Carbon-12 contains 6 protons and 6 neutrons. The radius of the nucleus is approximately $2.7 \mathrm{fm},$ and the radius of the atom is approximately $70 \mathrm{pm} .$ Calculate the volume of the nucleus and the volume of the atom. What percentage of the carbon atom's volume does the nucleus occupy?

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Key Concepts

Volume Ratio of Nucleus to Atom

This involves computing the ratio of the nucleus's volume to the entire atom's volume using their respective volumes derived from the volume formula for spheres. It underscores the idea that despite the nucleus holding most of the atom’s mass, it occupies only a tiny fraction of its total volume.

Nuclear and Atomic Structure

This concept deals with the understanding that the nucleus, which contains protons and neutrons, is a very small and dense core of the atom, while the electron cloud, which surrounds the nucleus, occupies a much larger volume. This disparity in size is crucial for comprehending the physical structure of atoms.

Volume of a Sphere

This concept involves using the mathematical formula V = (4/3)?r³ to compute the volume of a sphere given its radius. It is a fundamental concept in geometry that is directly applicable in calculating the volumes of both the atomic nucleus and the atom.

Unit Conversion and Order of Magnitude

In atomic and nuclear physics, distances are often given in very small units such as femtometers (fm) for nuclei and picometers (pm) for atoms. Understanding how to convert between these units and appreciating their orders of magnitude is essential when performing calculations that compare the sizes of different parts of an atom.

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