Question

One gram of gold costs \[ \$ 75 \]. How much would one atom of gold be worth?

Answer 1

Hint: To find out the worth of one atom of gold we will first have to calculate moles of gold, for that we will convert mass into moles. Then we will convert the moles into atoms of gold and then we can find the price of one atom of gold.

Complete step by step answer:
Lets try to solve this with given information
As we know mass of gold, Lets convert that mass into moles
 $ 1gAu \times \dfrac{{1mol\,Au}}{{197.0g\,Au}} = 5.076 \times {10^{ - 3}}mol\,Au $
Now we can convert moles into atoms of gold
 $ 5.076 \times {10^{ - 3}}mol\,Au \times \dfrac{{6.022 \times {{10}^{23}}atoms\,Au}}{{1mol\,Au}} = 3.057 \times {10^{21}}atoms\,Au $
So we can find worth of one atom of $ Au $
\[ \dfrac{{\$ 75}}{{3.057 \times {{10}^{21}}atoms\,Au}} \times 1atom\,Au = \$ 2.5 \times {10^{ - 20}} \]
The price for one atom of gold is \[ \$ 0.00000000000000000025 \].

Note:
To calculate the number of atoms in any given material, we first divide the weight which should be in grams by the amu atomic mass given in the periodic table for the given material then multiply it by Avagadro’s number.