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

Md Ariful Islam

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$color(white)(XX)$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 $color(orange)"(average atomic mass)"$

$79.904%=x+(1-x)$

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

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

$79.904%=78.92x+80.92-80.92x$

$79.904%=-2x+80.92$

$79.904%-80.92=78.92x$

$-1.016=-2x$

$x=0.508$

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%

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