Final answer:
To scale a nucleus to the size of a pencil eraser, the diameter of an atom would be approximately 104.17 feet, considering the atom's diameter is about 10,000 times larger than that of its nucleus.
Step-by-step explanation:
To create a scale model of an atom based on the given comparison, we need to consider the relative sizes of the nucleus and the entire atom. The diameter of a typical medium-sized nucleus is mentioned as being approximately 10 femtometers (10-14 meters), and the diameter of a typical atom is on the order of 100 picometers (10⁻¹⁰ meters). This indicates that an atom's diameter is about 10,000 times larger than that of its nucleus.
If we are scaling up the nucleus to the size of an eraser with a diameter of 0.125 inches, to maintain the same scale for the entire atom, we would need to also scale it up by a factor of 10,000. Therefore, to find the diameter of the atom in feet, we would do the following calculation:
0.125 inches (diameter of the nucleus at this scale) X 10,000 (scale factor) = 1,250 inches
There are 12 inches in a foot, so we convert 1,250 inches to feet:
1,250 inches / 12 inches per foot = 104.17 feet (rounded to two decimal places)
This calculation shows that at the scale where the nucleus is the size of a pencil eraser, the diameter of the atom would be approximately 104.17 feet.