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

1 Answer
Mar 24, 2018

Isotopes#color(white)(XX)#mass(amu)#color(white)(X)#Isotopic abundance

Br-79#color(white)(XXXX)#78.92#color(white)(XXXXXXX)#?

Br-81#color(white)(XXXX)#80.92#color(white)(XXXXXXX)#?

#"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 #color(orange)"(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=-2x#

#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"#

#:.# 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%