# An element has three naturally occurring isotopes with the following masses and abundances. How do you calculate the atomic mass of this element? What is the identity of the element?

## Isotopic Mass (amu) Fractional Abundance 38.964 0.9326 39.964 $1.000 \times {10}^{- 4}$ 40.962 0.0673

Aug 31, 2016

The element is potassium, and its atomic mass is 39.10 u.

#### Explanation:

The atomic mass is the weighted average of the atomic masses of each isotope.

In a weighted average, we multiply each value by a number representing its relative importance.

In this problem, the fractional abundance represents the relative importance of each isotope.

Here's how to do the calculation:

$\boldsymbol{\text{Atomic Mass/u" color(white)(m)bb"Fractional abundance" color(white)(m)bb"Contribution/u}}$
$\textcolor{w h i t e}{m m l} 38.964 \textcolor{w h i t e}{m m m m m m} 0.9326 \textcolor{w h i t e}{m m m m m m m m m m m} 36.338$
color(white)(mml)39.964color(white)(mmmmmm)1.000 × 10^"-4"color(white)(mmmmmmmmll)"0.003 996"
$\textcolor{w h i t e}{m m l} 40.962 \textcolor{w h i t e}{m m m m m m} 0.0673 \textcolor{w h i t e}{m m m m m m m m m m m l} 2.7567$
color(white)(mmmmmmmmmmmmmm)"Atomic mass = " color(white)(mmm) stackrel(———)(39.10)

The atomic mass of the element is 39.10 u.

The element is potassium.