Problems like this are meant to show how overwhelmingly large Avogadro's number is (and so, how small atoms and molecules are). They also provide some practice at solving problems that involve conversion of abstract units.
The 5-step method for converting units outlined in the measurement notes can be used to solve this problem.
- Estimate the area that one marble would cover.
- 10 marbles would cover 10 times that area; 100 marbles would cover 100 times the area of one marble. So how much total area would be covered by a mole (Avogadro's number, 6.02 × 1023) of marbles? Assume that they're spread out in a layer one marble deep.
- Calculate the number of layers of marbles that would cover the country by dividing the total area of the marbles by the area of the United States.
- If you know how deep each layer is, you can calculate the total depth.
Author: Fred Senese email@example.com