The concept of the mole is a foundational idea in chemistry, representing a specific and immense quantity of particles. Named for the Italian scientist Amedeo Avogadro, this unit defines an amount of substance containing exactly \(6.022 \times 10^{23}\) constituent entities, a value known as Avogadro’s number. While typically used to count atoms or molecules, applying this number to macroscopic objects like basketballs reveals a scale beyond everyday comprehension and illustrates the magnitude of this fundamental counting unit.
The Unit of Measurement
For this exercise, the unit is a standard size 7 regulation basketball, the official size used in men’s professional and college leagues. This ball has a diameter of approximately 9.4 inches, which translates to 24 centimeters. A regulation size 7 basketball has a mass of about 22 ounces, or 624 grams (0.624 kilograms). These specific measurements are used to calculate the total mass and volume of the mole collection.
Visualizing the Volume
The volume of a single basketball is small, but multiplying it by Avogadro’s number yields an astronomical total volume of approximately \(4.36 \times 10^{12}\) cubic kilometers. This total volume dramatically reshapes our perspective of planetary scale. For instance, if the entire mole of basketballs were formed into a single giant sphere, it would be large enough to contain more than four planet Earths inside it, given Earth’s volume of \(1.083 \times 10^{12}\) cubic kilometers.
If this immense collection were spread evenly across the Earth’s entire surface, including all the oceans, the layer would be a profound blanket. The depth of this layer would be over 8,500 kilometers deep, a distance greater than the radius of the Earth itself. This means the basketballs would not just cover the planet but would form a new, massive sphere around the core.
Considering a linear arrangement provides a staggering sense of the number’s scale. If all \(6.022 \times 10^{23}\) basketballs were lined up end-to-end, the chain would extend for about \(1.45 \times 10^{20}\) kilometers. For perspective, the farthest planet in our solar system, Neptune, is only about \(4.5\) billion kilometers away from Earth.
The line of basketballs would stretch far beyond the solar system and outside our galaxy. One light-year is the distance light travels in a year, or about \(9.46 \times 10^{12}\) kilometers. The line of basketballs would measure over 15 million light-years long, reaching deep into intergalactic space.
Mass and Counting the Collection
The total mass of this basketball collection provides another metric for grasping the number’s magnitude. Multiplying the mass of a single basketball (0.624 kg) by the mole results in a total mass of approximately \(3.76 \times 10^{23}\) kilograms. This mass is about 6.3% of the entire mass of the Earth.
The Moon is a more comparable object, with a mass of approximately \(7.35 \times 10^{22}\) kilograms. The mole of basketballs is over five times more massive than the Moon. This collection would exert a gravitational pull stronger than our natural satellite, significantly altering the dynamics of the Earth-Moon system.
The effort required to count this collection illustrates its practical impossibility. If every person on Earth (eight billion individuals) began counting the basketballs at a rate of one per second, the task would still take an astonishingly long time. The entire world population, counting simultaneously, would need nearly 2.4 million years to finish counting all \(6.022 \times 10^{23}\) basketballs.