Final answer:
If Earth had the same density as atomic nuclei, its radius would hypothetically be about 200 meters, significantly smaller than its actual radius of approximately 6.4 × 10⁶ meters.
Step-by-step explanation:
The question asks about the potential size of the Earth if its density were equal to that of atomic nuclei. Atomic nuclei are incredibly dense, with a density averaging about 1.8 × 10¹⁴ grams per cubic centimeter. Given that the actual mass of the Earth is 5.97 × 10²⁴ kg, if it had the density of nuclei, it would be significantly smaller.
For comparison, nuclei are much denser than any material we encounter in bulk form. Iridium, for instance, which is one of the densest elements we know of, has a density of only 22.6 g/cm³. Water's density is approximately 1 g/cm³.
Considering the actual radius of the Earth is about 6.4 × 10⁶ meters, and using the average density of nuclei, we can estimate the Earth's size if it had the same density. However, this calculation is quite complex and would result in a very small Earth, hypothetically only about 200 meters in radius, which is 30,000 times smaller than its current radius.