Assume a hydrogen atom is a sphere with diameter 0.100 nm...

Assume a hydrogen atom is a sphere with diameter $0.100 \mathrm{nm}$ and a hydrogen molecule consists of two such spheres in contact. (a) What fraction of the space in a tank of hydrogen gas at $0^{\circ} \mathrm{C}$ and 1.00 atm is occupied by the hydrogen molecules themselves? (b) What fraction of the space within one hydrogen atom is occupied by its nucleus, of radius $1.20 \mathrm{fm} ?$

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Key Concepts

Volume Fraction

The volume fraction is the ratio of the volume occupied by a component (such as a molecule or nucleus) to the total volume of a system or container. This concept is critical for understanding how much of a given space is physically taken up by the constituent objects, as opposed to being empty space.

Scale Comparison in Physics

Scale comparison involves studying how different physical dimensions vary by many orders of magnitude, such as comparing the size of an atom to the size of its nucleus. This is essential for understanding the relative sizes and distributions of different components within a system, highlighting the vast differences between atomic and subatomic scales.

Ideal Gas Law

The Ideal Gas Law relates pressure, volume, temperature, and the number of particles in a gas. It provides the conceptual framework for determining how many molecules are present in a given volume of gas under specified conditions, which is essential for calculating the physical space occupied by the gas particles.

Sphere Volume Calculation

This concept involves using the mathematical formula for the volume of a sphere, V = (4/3)?r³, to compute the space occupied by spherical objects. It is a fundamental tool for estimating the volume of atoms or molecules when they are approximated as spheres in various physical and chemical contexts.

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