The nucleus of a hydrogen atom is a single proton, which has a radius of about 1.0 10-15 m. The single electron in a hydrogen atom normally orbits the nucleus at a distance of 5.3 10-11 m. What is the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom?

Question

(density of nucleus / density of atom)

density = mass/volume
Use the exact mass of the H atom (and is this protium or all of the isotopes averaged?). You are given th volume. Calculate density of the nucleus from these values.

For the entire atom, add the mass of the electron to the mass of the proton you have used from above, and divide that combined mass by the volume listed in the problem. Calculate the density of the atom. Note: You aren't give the volume but the radius. Volume of sphere = 4/3*pi*r³.
Finally, commpute the ratio as you have noted.

The volume of a sphere is
(4/3)*pi*r³.