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29 July, 07:11

Gallium has two naturally occurring isotopes (Ga-69 and Ga-71) and has an atomic mass of 69.723 amu. The mass of Ga-71 is 70.925 amu, and its natural abundance is 39.892%.

Calculate the atomic mass (in amu) and natural abundance (in %) of the second isotope.

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  1. 29 July, 07:30
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    The answers are:

    - natural abundance: 60.108%

    - atomic mass: 68.926 amu

    The atomic mass of an element is the average of the atomic masses of its isotopes. The relative abundance of isotopes must be taken into consideration, therefore:

    atomic mass of copper = atomic mass of isotope 1 * abundance 1 + atomic mass of isotope 2 * abundance 2

    We know:

    atomic mass of copper = 69.723 amu

    The atomic mass of Ga-71 is: 70.925 amu

    The abundance of Ga-69 is: 39.892% = 0.39892

    The atomic mass of Ga-69 is: x

    The abundance of Ga-69 is: 100% - 39.892% = 60.108% = 0.60108

    Thus:

    69.723 amu = 70.925 amu * 0.39892 + x * 0.60108

    69.723 amu = 28.293 amu + 0.60108x

    ⇒ 69.723 amu - 28.293 amu = 0.60108x

    ⇒ 41.430 amu = 0.60108x

    ⇒ x = 41.430 amu : 0.60108 = 68.926 amu
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