# How would you calculate the atomic mass of rubidium given the two isotopes of rubidium have atomic masses and relative abundances of 84.91 amu (72.16%) and 86.91 amu (27.84%)?

Nov 17, 2015

$\text{85.47 u}$

#### Explanation:

The average atomic mass of an element is determined by taking the weighted average of the atomic masses of its naturally occurring isotopes.

Now, weighted average simply means that each isotope contributes to the average atomic mass of the element proportionally to its percent abundance.

color(blue)("avg. atomic mass" = sum_i ("isotope"_i xx "abundance"_i))

The more abundant an isotope is, the more its atomic mass will influence the average atomic mass of the element.

In your case, you know that rubidium has two stable isotopes

• $\text{^85"Rb" -> "84.91 u}$, 72.16% percent abundance
• $\text{^87"Rb" -> "86.91 u}$, 27.84% percent abundance

When you calculate the average atomic mass, make sure that you use decimal abundance, which is simply percent abundance divided by $100$.

So, plug in your values to get

$\text{avg. atomic mass" = "84.91 u" xx 0.7216 + "86.91 u} \times 0.2784$

$\text{avg. atomic mass " = " 85.4668 u}$

Rounded to four sig figs, the answer will be

"avg. atomic mass " = color(green)(" 85.47 u")