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20 April, 21:39

Elemental magnesium consists of three isotopes: 24mg with an accurate mass of 23.99 amu, 25mg with an accurate mass of 24.99 amu, and 26mg with an accurate mass of 25.99 amu. if 24mg is 79% of naturally occurring magnesium, what is the percent abundance of 26mg?

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  1. 20 April, 22:56
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    The relative abundances of the three isotopes must be equal to 1. Suppose x is the abundance of 25 mg, and y is the abundance of 26 mg, then,

    x + y + 0.79 = 1 - - > eqn 1

    The average atomic weight of Magnesium is 24.305 amu. Thus,

    23.99 (0.79) + 24.99 (x) + 25.99 (y) = 24.305 - - > eqn 2

    Rearranging eqn 1: x = 1 - 0.79 - y = 0.21 - y. Substituting this to the second equation,

    23.99 (0.79) + 24.99 (0.21 - y) + 25.99 (y) = 24.305

    Solving for y,

    y = 0.105 or 10.5%

    Thus, the percent abundance of 26 mg is y which is 10.5%.
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