Final answer:
To calculate the depth to which Avogadro's number of table tennis balls would cover Earth, we need to find the volume of one ball, calculate the effective volume including the space between the balls, multiply it by Avogadro's number, and then divide it by the surface area of the Earth. The correct answer is option A) 26,194 km.
Step-by-step explanation:
To calculate the depth to which Avogadro's number of table tennis balls would cover Earth, we need to find the volume of one table tennis ball and then multiply it by Avogadro's number. First, we calculate the volume of one ball by using the formula for the volume of a sphere: V = (4/3)πr^3. Given that the diameter of each ball is 3.75 cm, the radius is half of that, which is 1.875 cm or 0.01875 m. Plugging this value into the formula, we find that the volume of one ball is approximately 0.002214 m³. Next, we need to account for the extra space between the balls, which adds 25.0% to their volume. So, the effective volume of each ball would be 1.25 times the volume we calculated earlier. Now we can multiply the effective volume of one ball by Avogadro's number (approximately 6.022 × 10^23) to find the total volume that Avogadro's number of balls would cover. Multiplying these values, we get a total volume of approximately 0.013343 m³. Finally, to find the depth, we divide this volume by the surface area of the Earth. The surface area of Earth is approximately 510,100,000 km² or 510,100,000,000,000 m². Dividing the total volume by the surface area, we get a depth of approximately 26,193.8 km. Therefore, the correct answer is option A) 26,194 km.