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:

$\begin{gathered} \frac{1}{4000}=\frac{3.25\times10^{-22}g}{x} \\ x=4000\cdot3.25\times10^{-22}g \\ x=13000\times10^{-22}g \end{gathered}$

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

$13000\times10^{-22}g=1.3\cdot10^4\times10^{-22}g=1.3\times10^{-18}g$

So, the mass is

$1.3\times10^{-18}g$