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31 August, 20:57

The atomic weight of silver is 107.868 amu. Naturally occurring silver consists of two isotopes. 107Ag (mass = 106.904 amu) and 109Ag (mass = 108.905 amu). What percentage of naturally occurring silver is the heavier isotope? a. 45.4% b. 52.6% c. 62.7% d. 48.2% e. 51.7%

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  1. 31 August, 22:15
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    The heavier isotope is 48.2 % (option d)

    Explanation:

    Step 1: Data given

    Atomic weight of silver = 107.868 amu

    Isotopes of silver:

    107Ag = 106.904 amu

    109Ag = 108.905 amu

    Step 2: Calculate the percentages

    107.868 = 106.904 * x + 108.905 * y

    x+y = 1 ⇒ x = 1 - y

    107.868 = 106.904 (1 - y) + 108.905*y

    107.868 = 106.904 - 106.904y + 108.905y

    0.964 = 2.001y

    y = 0.4818

    x = 1 - 0.4818 = 0.5182

    Percentage 109Ag = 48.18 %

    Percentage 107Ag = 51.82 %

    The heavier isotope is 109Ag. Its percentage is 48.18 ≈ 48.2 %
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