Question

An atom of gold has a mass of approximately 3.25 x 10-22 grams. What is the mass of 4000 atoms ofgold? Express your answer in scientific notation.AnswerKeypadKeyboard ShortcutsX10grams

Answer 1

The mass of a certain quantity of atoms of gold is directly proportional to the number of atoms of gold.

Thus, we can use rule of three to calculate the answer.

1 atom of gold has a mass of approximately 3.25 x 10⁻²² g.

4000 atoms of gold will have a mass of x.

1 atom ---- 3.25 x 10⁻²² g

4000 atoms ---- x

Thus:

`\begin{gathered} (1)/(4000)=(3.25*10^(-22)g)/(x) \\ x=4000\cdot3.25*10^(-22)g \\ x=13000*10^(-22)g \end{gathered}`

Now, we have to adjust the coefficient so that it comes back to scientific notation:

`13000*10^(-22)g=1.3\cdot10^4*10^(-22)g=1.3*10^(-18)g`

So, the mass is

`1.3*10^(-18)g`