## Related questions with answers

Bromine has two naturally occurring isotopes $(\mathrm{Br}-79$ and Br-$81$) and an atomic mass of $79.904$ amu.

(a) If the natural abundance of $\mathrm{Br}-79$ is $50.69 \%$, what is the natural abundance of Br-$81$?

(b) If the mass of Br-$81$ is $80.9163 \mathrm{amu}$, what is the mass of Br-$79$?

Solution

Verified$\textbf{a.}$ The sum of all relative abundances of all isotopes of an element has to be equal to 100%.

$\begin{equation} 100 \% = \sum^{n}_{i=1}{X_{i}} \end{equation}$

Where $n$ is the number of all naturally occurring isotopes and $X_{i}$ is the relative abundance of a particular isotope.

So for this example. There are two naturally occurring isotopes ($n=2$). If we know the abundance of one of them, we can calculate the abundance of the other:

$\begin{equation} 1 = X_{Br-79} + X_{Br-81} = 0,5069 + X_{Br-81} \end{equation}$

Using simple algebra we can calculate $X_{Br-81}$

$\begin{equation} X_{Br-81} = 1-0,5069 = 0,4931 = 49,31\% \end{equation}$

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