What experimental evidence led Rutherford to conclude the following? (a) The nucleus of the atom contains most of the atomic mass. (b) The nucleus of the atom is positively charged. (c) The atom consists of mostly empty space.

Understanding the atomic nucleus composition is pivotal to grasping the fundamentals of atomic physics. Through his pioneering Gold Foil experiment, Rutherford made groundbreaking observations concerning the nucleus. Alpha particles, or helium nuclei, were observed to pass straight through gold foil with minimal deflection, an indication that the nucleus, which contain most of the atom's mass, occupies just a small fraction of the atom's volume. This dense central region suggested a significant concentration of mass, contrasting the previously accepted 'plum pudding' model which proposed a uniform spread of mass and charge. Thus, the atomic nucleus composition was understood to be compact, with considerable mass relative to the entire atom.

These findings laid the groundwork for later developments, leading to the discovery of protons contained within the nucleus. This crucial insight shifted the view of atomic structure from a sea of charge to one where mass and positive charge are central, encircled by a relatively large empty space where electrons reside.

The concept of nuclear charge is integral to the explanation of atomic structure and behavior. Rutherford's observation of the deflection patterns of alpha particles—which are themselves positively charged—revealed that they were repelled by an intense positive charge during his Gold Foil experiment. Since like charges repel, this repulsion highlighted the presence of a concentrated positive charge within the nucleus, which we know as protons. The degree of deflection of these alpha particles by the gold foil was pivotal in concluding the nucleus's positive charge.

Moreover, if the gold atom had no positive nucleus, the alpha particles would pass through unimpeded, however, significant deflections, albeit in a minuscule number of instances, demonstrated the presence of this concentrated nuclear charge. This understanding has since played a key role in the development of atomic models and has mathematical implications when calculating the force between charged particles, including the important concept of Coulomb's law.

Delving into the atomic structure, Rutherford's experiment countered the then-prevalent belief of atoms being uniformly packed spheres of positive charge wherein electrons were distributed. Unlike Thomson's 'plum pudding' model, Rutherford proposed that atoms are mostly empty space with a densely packed central nucleus. This alteration in atomic theory reshaped the understanding of how atoms are put together and how they interact with one another.

Through Rutherford's interpretation of his experiment's results, it became clear that the almost undisturbed passage of most alpha particles indicated vast empty areas within the atom. Such information fortified the concept that electrons orbit around a central nucleus, analogous to planets orbiting the sun, albeit in a quantum mechanical framework rather than classical orbits. This breakthrough firmly grounded the planetary model of the atom and subsequently led to the development of quantum mechanics, which provided a more complex and accurate depiction of electron behavior and atomic structure.