Question

The thickness/height of aluminum foil is 0.00122 cm. The diameter of an aluminum atom is 3.0 × 10⁻⁸ cm. Assuming they're stacked up on each other, how many atoms thick is the foil? You have to use dimensional analysis and express your answer with the right amount of significant figures.

Answer 1

The aluminum foil is approximately 4.1 × 10⁴ atoms thick, calculated by dividing the thickness of the foil by the diameter of an aluminum atom and expressing the result with the correct number of significant figures.

Step-by-step explanation:

When determining how many atoms thick the aluminum foil is, we must divide the thickness of the foil by the diameter of an aluminum atom. We calculate the thickness in atoms as follows:

(0.00122 cm) / (3.0 × 10⁻⁸ cm/atom) = 4.066 × 10⁴ atoms.

However, we need to adjust the result for the correct number of significant figures, based on the provided measures. Both the thickness of the foil and the diameter of an aluminum atom have two significant figures, so our result should also be reported with two significant figures: 4.1 × 10⁴ atoms.

Therefore, the aluminum foil is approximately 4.1 × 10⁴ atoms thick.