# Bromine consists of two isotopes with masses of 78.92 and 80.92 amu. What is the abundances of these two isotopes?

Mar 24, 2018

Isotopes$\textcolor{w h i t e}{X X}$mass(amu)$\textcolor{w h i t e}{X}$Isotopic abundance

Br-79$\textcolor{w h i t e}{X X X X}$78.92$\textcolor{w h i t e}{X X X X X X X}$?

Br-81$\textcolor{w h i t e}{X X X X}$80.92$\textcolor{w h i t e}{X X X X X X X}$?

"average atomic mass"=("mass*%"+"mass*%"+"mass*%"...)

Let x be % abundance of Br-79

Let 1-x be % abundance of Br-81

Br is 79. 904g/mol on the periodic table $\textcolor{\mathmr{and} a n \ge}{\text{(average atomic mass)}}$

79.904%=x+(1-x)

79.904%=(78.92*x)+(80.92*(1-x))

79.904%=(78.92x)+(80.92-80.92x))

79.904%=78.92x+80.92-80.92x

79.904%=-2x+80.92

79.904%-80.92=78.92x

$- 1.016 = - 2 x$

$x = 0.508$

Use our x to find that % abundance of Br-79

x*100%

0.508*100%

$= 50.8$ "% abundance"

Use our x to find that % abundance of Br-79

(1-x)*100%

0.492*100%

$= 49.2$ "% abundance"

$\therefore$ The % abundance of the isotope with a mass of 78.92 amu has a % abundance of 50.8% and the isotope with a mass 80.92 amu has a % abundance of 49.2%