(a) Assuming the dimensions of the nucleus and atom shown in Figure 2.10, what fraction of the volume of the atom is taken up by the nucleus?

Verified step by step guidance

1. insert step 1: Understand the problem by identifying the given information. You need the dimensions of both the nucleus and the atom. Assume the nucleus is a sphere with radius r_nucleus and the atom is a sphere with radius r_atom.
2. insert step 2: Use the formula for the volume of a sphere, V = \frac{4}{3}\pi r^3, to calculate the volume of the nucleus.
3. insert step 3: Similarly, use the same formula to calculate the volume of the atom.
4. insert step 4: Determine the fraction of the volume of the atom that is occupied by the nucleus by dividing the volume of the nucleus by the volume of the atom.
5. insert step 5: Simplify the expression to find the fraction, which will be a very small number, indicating that the nucleus occupies a tiny fraction of the atom's volume.

Key Concepts

Atomic Structure

Atoms consist of a nucleus, which contains protons and neutrons, surrounded by electrons in various energy levels. The nucleus is significantly smaller than the entire atom, which includes the electron cloud. Understanding the relative sizes of these components is crucial for calculating volume fractions.

Volume Calculation

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. To find the fraction of the atom's volume occupied by the nucleus, one must calculate the volumes of both the atom and the nucleus and then divide the nucleus's volume by the atom's volume.

Fractional Volume

The fractional volume is a ratio that compares the volume of a part to the total volume. In this context, it is the volume of the nucleus divided by the volume of the atom, expressed as a decimal or percentage. This concept helps quantify how much space the nucleus occupies relative to the entire atom.