A hydrogen atom has a diameter of $1.06\times 10^{-10}\mathrm{m}.$ The nucleus of the hydrogen atom has a diameter of approximately $2.40\times 10^{-15}\mathrm{m}.$ (a) For a scale model, represent the diameter of the hydrogen atom by the playing length of an American football field (100 yards = 300 ft) and determine the diameter of the nucleus in millimeters. (b) Find the ratio of the volume of the hydrogen atom to the volume of its nucleus.

Key Concepts: Atomic Structure, Scaling, Volume Explanation: The question asks us to create a scale model of the hydrogen atom and determine the diameter of its nucleus. It then asks for the ratio of the volume of the hydrogen atom to the volume of its nucleus. Step by Step Solution: Step 1. Convert the diameter of the hydrogen atom in meters to yards by dividing by 0.9144 (1 meter = 1.09361 yards). Step 2. Scale the diameter of the hydrogen atom down to the length of an American football field, which has a playing length of 100 yards. Step 3. Determine the diameter of the nucleus in millimeters using scientific notation. Step 4. Calculate the ratio of the volume of the hydrogen atom to the volume of its nucleus using the formula for the volume of a sphere (V = (4/3)πr^3) and the diameters of the two spheres. Final Answer: The diameter of the hydrogen atom in yards is 0.1162 yards. The diameter of the nucleus is 2.61 × 10^(-5) millimeters. The ratio of the volume of the hydrogen atom to the volume of its nucleus is approximately 6.4 × 10^13.