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.