# How do I calculate average atomic mass?

## The question I am stuck on is: A silver sample contains 52 atoms, each having 60 neutrons, and 48 atoms, each having 62 neutrons. What is the sample's average atomic mass? Please, break it down step by step and explain why, thank you.

Mar 1, 2016

$\text{107.96 u}$

#### Explanation:

The thing to remember about an element's average atomic mass is that each isotope will contribute proportionally to its abundance.

In simple terms, the average atomic mass of element is calculated by taking the weighted average of the atomic mass of its stable isotopes.

The more abundant an isotope is, the more it will contribute to the average atomic mass of the element.

$\textcolor{b l u e}{{\text{avg. atomic mass" = sum_i "isotope"_i xx "abundance}}_{i}}$

In the actual calculation of the average atomic mass you use decimal abundances, which are simply percent abundances divided by $100$.

So, you know that you're dealing with a sample of silver atoms. Out of this sample, $52$ atoms have $60$ neutrons and $48$ atoms have $62$ neutrons.

The total size of the sample is $100$ atoms, which will make the decimal abundance calculations easier.

Now, do not forget that the atomic mass of an isotope is approximately equal to the number of protons and neutrons that isotope has in its nucleus.

Pick up a periodic table and look for silver, $\text{Ag}$. Notice that its atomic number is equal to $47$. This means that every isotope of silver will have $47$ protons in its nucleus.

The first isotope will thus have an atomic mass of

$\text{47 protons " + " 60 neutrons" = "107 u}$

The second isotope will have an atomic mass of

$\text{47 protons " + " 62 neutrons" = "109 u}$

So, $52$ out of $100$ atoms have an atomic mass of $\text{107 u}$. The decimal abundance for this first isotope will be

$\frac{52}{100} = 0.52$

The other $48$ atoms have an atomic mass of $\text{109 u}$. The decimal abundance of the second isotope will be

$\frac{48}{100} = 0.48$

This means that the average atomic mass of silver is

$\text{avg. atomic mass" = "107 u" xx 0.52 + "109 u} \times 0.48$

"avg. atomic mass " = color(green)(" 107.96 u")