Silver has two naturally occurring isotopes with the following isotopic masses: 10747Ag 10947Ag 106.90509 108.9047 The average atomic mass o

Question

Silver has two naturally occurring isotopes with the following isotopic masses: 10747Ag 10947Ag 106.90509 108.9047 The average atomic mass of silver is 107.8682 amu. The fractional abundance of the lighter of the two isotopes is ________.

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Latifah 3 years 2021-07-14T02:01:54+00:00 1 Answers 38 views 0

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  1. Dulcie
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    2021-07-14T02:03:06+00:00
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    Answer: The fractional abundance of lighter isotope is 0.518

    Explanation:

    Average atomic weight is the sum of the masses of the individual isotopes each multiplied by its fractional abundance. The equation used is:\text{Average atomic weight}=\sum_{i=1}^{n}\text{(Atomic mass of isotope)}_i\times \text{(Fractional abundance)}_i           ……(1)

    Let the fractional abundance of Ag-107 isotope be ‘x’

    • For Ag-107 isotope:

    Atomic mass = 106.90509 amu

    Fractional abundance = x

    • For Ag-109 isotope:

    Atomic mass = 108.9047 amu

    Fractional abundance = (1 – x)

    Average atomic mass of silver = 107.8682 amu

    Plugging values in equation 1:

    107.8682=(106.90509 \times x) + (108.9047 \times (1-x))\\\\107.8682=106.90509x+108.9047-108.9047x\\\\1.99961x=1.0365\\\\x=0.518

    Fractional abundance of Ag-107 isotope (lighter) = x = 0.518

    Hence, the fractional abundance of lighter isotope is 0.518

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