Question

There is relatively little empty space between atoms in solids and liquids, so that the average density of an atom is about the same as matter on a macroscopic scale–approximately 1,000 kg/m³. The nucleus of an atom has a radius about 10⁻⁵ times that of the atom and contains nearly all the mass of the entire atom. What is the approximate density of a nucleus?

Answer 1

The density of an atomic nucleus is approximately 1.8 × 10¹⁷ kg/m³, which is about 2 × 10¹⁴ times greater than the density of water.

Step-by-step explanation:

The question asks to calculate the approximate density of a nucleus. We know that the average density of matter at a macroscopic scale is about 10³ kg/m³ and that the density of the nucleus is much greater since it contains nearly all the mass of the atom within a much smaller volume. Given that the radius of the nucleus is about 10⁻¹⁵ m, compared to the atom's radius of approximately 10⁻¹⁰ m, and taking into account the dense packing of protons and neutrons within the nucleus, the average nuclear density is 1.8 × 10¹⁴ grams per cubic centimeter, or 1.8 × 10¹⁷ kg/m³.

The density of the nucleus is thus roughly 2 × 10¹⁴ times greater than that of water (which has a density of 1,000 kg/m³). This high density reflects the compactness of nuclear matter, which is also exemplified by objects such as neutron stars, remnants of supernovas.