Final answer:
The calculation compares the density of a solar mass black hole with that of an iron nucleus by first finding the density of the iron nucleus using its mass and radius and then considering the density within the event horizon of the black hole based on astronomical observations and general relativity.
Step-by-step explanation:
Calculating the ratio of the mass density of a solar mass black hole to that of an iron nucleus involves determining the density for both objects and then comparing them. For the iron nucleus with a given mass and radius, its density (ρ) is given by the formula ρ = mass/volume, where the volume (V) is calculated using the formula for the volume of a sphere (V = 4/3πr³). Given that the mass of an iron nucleus is 56 * 1.66×10⁻²⁷ kg and the radius is 1.2×10⁻¹⁵ * 56¹/³ m, we can calculate its density.
The density of a solar mass black hole is significantly more complex because it involves understanding the concept of event horizons and Schwarzschild radii. Black holes have incredibly high densities due to their immense mass being concentrated within a very small volume dictated by their event horizon. To accurately compare densities, we make use of general relativity and astronomical observations.