The statement that the nucleus of an atom contains heavy mass within a small volume is based on experimental observations and the understanding of atomic structure.
Atoms are composed of a central nucleus and electron(s) orbiting around it. The nucleus is located at the center of the atom and contains most of the atom's mass. It is composed of protons and neutrons, which are collectively known as nucleons. Protons have a positive charge, while neutrons have no charge. Electrons, which are much smaller in mass compared to protons and neutrons, occupy the space around the nucleus.
Experimental evidence, such as the results of alpha particle scattering experiments conducted by Ernest Rutherford and his colleagues, led to the conclusion that the nucleus is small and dense. In these experiments, alpha particles (helium nuclei) were directed at a thin gold foil. Most of the alpha particles passed through the foil, but a small fraction were deflected at large angles or even bounced back. This observation indicated that the majority of the atom's mass is concentrated in a tiny, positively charged region within the atom, which is now known as the nucleus.
The fact that the nucleus contains heavy mass within a small volume can be understood by considering the relative masses and sizes of protons, neutrons, and electrons. Protons and neutrons are approximately 1,800 times more massive than electrons. However, electrons occupy a much larger volume compared to the nucleus because they exist in electron orbitals that extend far beyond the nucleus.
In summary, the statement that the nucleus of an atom contains heavy mass within a small volume is supported by experimental evidence, such as alpha particle scattering experiments, and the understanding of atomic structure based on our current understanding of subatomic particles.