Carbon-12 contains six protons and six neutrons. The radius...

Name: Problem 107, Chapter 2: Chemistry A Molecular Approach
Uploaded: 2021-10-22T18:01:32-08:00
Duration: 2 min 1 s
Channel: David Collins
Description: Carbon-12 contains six protons and six neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers) and the radius of the atom is approximately 70 pm (picometers). Calculate the volume of the nucleus and the volume of the atom. What percentage of the carbon atom's volume is occupied by the nucleus? (Assume two significant figures.)

Carbon-12 contains six protons and six neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers) and the radius of the atom is approximately 70 pm (picometers). Calculate the volume of the nucleus and the volume of the atom. What percentage of the carbon atom's volume is occupied by the nucleus? (Assume two significant figures.)

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Key Concepts

Volume Calculation Using the Sphere Formula

This concept involves using the mathematical formula for the volume of a sphere, which is (4/3)?r^3. It is essential for calculating the volume of both the nucleus and the atom, assuming they are spherical. This formula is broadly applicable in physical sciences for determining the space occupied by spherical objects and is a standard tool in geometrical calculations.

Unit Conversion and Orders of Magnitude

Unit conversion is critical when dealing with measurements at vastly different scales, such as femtometers for nuclei and picometers for atoms. Understanding and converting these units accurately helps compare sizes and volumes that differ by orders of magnitude. This is a fundamental aspect when analyzing physical dimensions in nuclear and atomic physics.

Percentage and Scale Comparisons

Calculating the percentage of the atom's volume occupied by the nucleus involves comparing two volumes to determine a relative proportion. This concept is important in demonstrating the vast difference in scale between the densely packed nucleus and the much larger electron cloud in an atom, emphasizing the understanding of relative size in physical and atomic structures.

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