Gold prices in early 2013 were approximately $51 per gram. Given that the mass of a gold atom is approximately [tex]3.27 \times 10^{-22}[/tex] grams, how many gold atoms could you buy with a quarter ($0.25)?

A. [tex]1.2 \times 10^{22}[/tex] atoms
B. [tex]1.5 \times 10^{19}[/tex] atoms
C. [tex]7.6 \times 10^{20}[/tex] atoms
D. [tex]6.5 \times 10^{19}[/tex] atoms
E. [tex]1.1 \times 10^{23}[/tex] atoms

Given the price of gold and the mass of a gold atom, we can calculate the number of gold atoms that can be bought with $0.25. After doing the math, the answer corresponds to option b: 1.5 x 10^19 atoms.

Explanation:

The first step to answering this question is to determine the number of gold atoms you can purchase with $1. Given a price of $51 per gram and a mass of 3.27 x 10⁻²² grams per gold atom, the number of gold atoms for $1 is $1 / $51 * (1 gram / 3.27 x 10⁻²² grams). Now, to determine how many gold atoms can be bought with a quarter ($0.25), we multiply our previous answer by 0.25. The answer is thus 1.5 x 10^19 atoms (option b). Therefore, we divide 0.0049 grams by 3.27 x 10⁻²² grams to get a result of approximately 1.5 x 10¹⁹ gold atoms. So, the correct answer is option b. 1.5 x 10¹⁹ atoms.

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