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19 October, 06:17

Boron has an average mass of 10.81. One isotope of boron has a mass of 10.012938 and a relative abundance of 19.80 percent. The other isotope has a relative abundance of 80.20 percent. What is the mass of the two isotopes?

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  1. 19 October, 07:51
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    The average mass of an atom is calculated with the formula:

    average mass = abundance of isotope (1) * mass of isotope (1) + abundance of isotope (2) * mass of isotope (2) + ... an so on

    For the boron we have two isotopes, so the formula will become:

    average mass of boron = abundance of isotope (1) * mass of isotope (1) + abundance of isotope (2) * mass of isotope (2)

    We plug in the values:

    10.81 = 0.1980 * 10.012938 + 0.8020 * mass of isotope (2)

    10.81 = 1.98 + 0.8020 * mass of isotope (2)

    10.81 - 1.98 = 0.8020 * mass of isotope (2)

    8.83 = 0.8020 * mass of isotope (2)

    mass of isotope (2) = 8.83 / 0.8020

    mass of isotope (2) = 11.009975

    mass of isotope (1) = 10.012938 (given by the question)
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