Calculating % Abundance of Br-79 & Br-81

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To calculate the percent abundance of the bromine isotopes Br-79 and Br-81, the atomic weights of both isotopes and the average atomic weight of bromine are used. The initial equation incorrectly assumes equal abundances for both isotopes, which is not the case. The correct approach involves using two variables to represent the different abundances and setting up a system of equations: one for the weighted average and another for the total abundance. The final results indicate that Br-79 has an abundance of approximately 50.66% and Br-81 about 49.33%. This method ensures accurate calculations for isotope abundance based on their respective weights.
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Homework Statement


Naturally occurring bromine contains two isotopes; Br-79, which has a weight of 78.9183 and Br-81 with a weight of 80.9163. If the atomic weight of Br is 79.904, determine the % abundance of Br-79 and Br-81.

Homework Equations



To solve this equation I try to put the equation as

(x)(78.9183) + (x)(80.9163) = 79.904

The value of x = .499946789



The Attempt at a Solution



The answers were given because this is a practical exam I'm studying for. Can someone point me in the right direction. Something seems to be missing from the equation.


Br-81 49.33%
Br-79 50.66%
 
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Nevermind I found the answer.. Thank you
 
For the record:

sjung915 said:
(x)(78.9183) + (x)(80.9163) = 79.904

is wrong, as abundances of both isotopes are different, not identical - so you need two variables. The correct equation is

(x1)(78.9183) + (x2)(80.9163) = 79.904

and you need another equation:

x1 + x2=1
 
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