Final Answer-Explanation:
To calculate the ratio of the radius of the uranium-238 nucleus to the proton of the hydrogen atom, we'll use the following data:
The radius of a uranium-238 nucleus (Ru238) is approximately 5.5 femtometers (1 femtometer = 10^-15 meters).
The radius of a proton (RH) is about 0.88 femtometers.
Now, let's calculate the ratio:
Ratio = Ru238 / RH
= 5.5 fm / 0.88 fm
≈ 6.25
So, the radius of the uranium-238 nucleus is approximately 6.25 times greater than the radius of the proton in the hydrogen atom.
Next, let's calculate the density comparison between an atomic nucleus and a piece of granite.
The density of uranium-238 can be used as a representative value for the atomic nucleus, which is approximately 19,050,000 kilograms per cubic meter.
Given the density of granite is approximately 2600 kilograms per cubic meter.
Now, let's calculate the density ratio:
Density ratio = Density of uranium-238 / Density of granite
= 19,050,000 kg/m^3 / 2600 kg/m^3
≈ 7317.3
This calculation demonstrates that the density of an atomic nucleus is approximately 7317 times greater than that of a piece of granite.
In summary, the radius of the uranium-238 nucleus is about 6.25 times greater than the radius of a proton in the hydrogen atom, and the atomic nucleus is approximately 7317 times denser than a piece of granite.
