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9 October, 04:49

There are two isotopes of boron: boron-10 and boron-11. Explain, in terms of weighted average atomic mass, the difference in percent abundance of each of the isotopes of boron.

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  1. 9 October, 05:58
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    Percent abundance of B¹⁰ is 19.9% and B¹¹ is 80.1%.

    The weighted average atomic mass of boron is 10.811 amu.

    Explanation:

    We know that average atomic mass of Boron is 10.811 amu and there are two isotopes of boron B¹⁰ (10.012938) and B¹¹ (11.009305)

    We will determine the percent abundance of each isotopes.

    First of all we will set the fraction for both isotopes B¹⁰ and B¹¹.

    X for the isotopes having mass 11.009305 amu.

    1-x for isotopes having mass 10.012938 amu.

    The average atomic mass of Boron is 10.811 amu

    we will use the following equation,

    11.009305x + 10.012938 (10.012938 - x) = 10.811

    11.009305x + 10.012938 - 10.012938 x = 10.811

    11.009305x - 10.012938 x = 10.811 - 10.012938

    0.996367x = 0.798062

    x = 0.798062 / 0.996367

    x = 0.800972

    Percent abundance of B¹¹.

    0.800972 * 100 = 80.1 %

    80.1 % is abundance of B¹¹ because we solve the fraction x.

    now we will calculate the abundance of B¹⁰.

    (1-x)

    1-0.800972 = 0.199

    Percent abundance of B¹⁰.

    0.199 * 100 = 19.9%

    19.9% for B¹⁰.

    Now we can calculate the average atomic mass of boron.

    Formula:

    Average atomic mass = [mass of isotope * its abundance] + [mass of isotope * its abundance] + ... [ ] / 100

    Now we will put the values in formula.

    Average atomic mass = [19.9 * 10.012938] + [80.1 * 11.009305] / 100

    Average atomic mass = 199.2575 + 881.8453 / 100

    Average atomic mass = 10.811 amu
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