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Chapter 29: Problem 55

The diameter of an atom is \(1.2 \times 10^{-10} \mathrm{m}\) and the diameter of its nucleus is \(1.0 \times 10^{-14} \mathrm{m} .\) What percent of the atom's volume is occupied by mass and what percent is empty space?

Short Answer

Expert verified
The mass occupies a very minute proportion of the atom's volume, with a large percentage being empty space. The exact figures would be obtained by following the steps, which include calculating the volumes of the atom and the nucleus, and determining their percentages in terms of each other.

Step by step solution

01

Calculate the volume of the atom

To get the volume of the atom, use the formula for the volume of a sphere \(\frac{4}{3}\pi r^3\). However, the radius should be used which is half of the diameter; thus the radius is \(0.6 \times 10^{-10} m\). Substituting that into the formula gives the volume of the atom.
02

Calculate the volume of the nucleus

Using the same volume formula, the volume of the nucleus can also be calculated. The radius of the nucleus, half of its diameter, is \(0.5 \times 10^{-14} m\). Substituting this into the volume equation gives the volume of the nucleus.
03

Calculate the proportion of the atom鈥檚 volume that is occupied by the nucleus

Having both volumes, the next step is calculating the percentage of the atom filled by the nucleus. Determine this by dividing the volume of the nucleus by the volume of the atom and multiplying the result by 100 to get a percentage.
04

Determine the proportion of the atom that is empty space

The remaining volume of the atom not occupied by the nucleus is the empty space. Subtract the percentage of the volume occupied by the nucleus from 100 to get the percentage of the atom that is empty space.

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If the nucleus is a few fm in diameter, the distance between the centers of two protons must be \(\approx 2 \mathrm{fm}\). a. Calculate the repulsive electric force between two protons that are \(2.0 \mathrm{fm}\) apart. b. Calculate the attractive gravitational force between two protons that are \(2.0 \mathrm{fm}\) apart. Could gravity be the force that holds the nucleus together?

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