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What are the natural abundances of 28Si and 30Si in the following mixture: A sample of naturally occurring silicon consists of 28Si (27.9769 amu,) 29Si (28.9765 amu,) and 30Si (29.9738 amu.) If the atomic mass of silicon is 28.0855 amu and the natural abundance of 29Si is 4.67%, what are the natural abundances of 28Si and 30Si?  

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A sample of naturally occurring silicon consists of 28Si that has a mass of 27.9769 amu, 29Si that has a mass of 28.9765 amu, and 30Si with a mass of 29.9738 amu. The atomic mass of silicon the sample is 28.0855 amu and the natural abundance of 29Si is 4.67%.

Let the abundance of 28Si be x%, the abundance of 30Si is (1 - 0.0467 - x). The mass of the sample is the weighted average of the the three constituents.

28.9765*0.0467 + 27.9769*x + 29.9738*(1 - 0.0467 - x) = 28.0855

=> 28.9765*0.0467 + 27.9769*x + 29.9738*0.9533 - 29.9738*x = 28.0855

=> 27.9769*x - 29.9738*x = 28.0855 - 28.9765*0.0467 -  29.9738*0.9533

=> x*-1.9969 = -1.84173

=> x = 0.922

1 - x - 0.0467 = 0.031

The abundance of 28Si is 92.2% and the abundance of 30Si is 3.1%

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