Final answer:
To determine if purchasing 1 trillion gold atoms for $5 is a good deal, the mass of gold that corresponds to the number of atoms must be calculated and compared to the current market price. Given that 1 trillion is much smaller than Avogadro's number, the cost of the gold is likely lower than $5, making it a great deal.
Step-by-step explanation:
The question asks whether it would be a good deal to buy 1 trillion gold atoms for $5, taking into account the current price of gold. To answer this question, one needs to consider both the mass of gold that 1 trillion atoms represent and its cost at the current market value.
One troy ounce of gold is equal to 31.103 grams, and with gold currently priced around $60,000 per kilogram, we can determine the cost of gold per gram and subsequently the cost for the amount represented by 1 trillion atoms.
Considering the atomic mass of gold (Au) is approximately 197 grams/mol and Avogadro's number is 6.022 x 10^23 atoms/mol, we can calculate the mass in grams of 1 trillion gold atoms and compare it to the cost of an equivalent mass based on the market value.
However, without doing the precise calculation, given the sheer size of Avogadro's number in relation to 1 trillion, we can infer that the mass corresponding to 1 trillion atoms of gold would be very small, and its market value will be much less than $5.
Therefore, option (a), 'Yes, it's a great deal', would likely be the correct answer as you're getting the gold for less than its market value. However, it must be noted that possessing such a small quantity of gold may not have practical value.