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3 December, 02:20

The element europium exists in nature as two isotopes: 151eu has a mass of 150.9196 amu, and 153eu has a mass of 152.9209 amu. the average atomic mass of europium is 151.96 amu. calculate the relative abundance of the two europium isotopes.

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  1. 3 December, 03:52
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    Two isotopes of europium are 151eu and 153eu

    Mass of 151eu = 150.9196 amu

    Mass of 153eu = 152.9209 amu

    Average atomic mass = 151.96 amu

    Let x and y are the relative abundance of two isotopes of europium are 151eu and 153eu

    So, x% times 150.9196 + y% times 152.9209 = 151.96

    x150.9196 + y152.9209 = 151.96

    And x + y = 100% = 1, from here x = 1 - y and y = 1 - x

    Solve these equation by substitution,

    By replacing x = 1-y, we get

    (1-y) 150.9196 + y152.9209 = 151.96

    150.9196 - 150.9196y + y152.9209 = 151.96

    2.0013y = 1.0404

    Y = 0.5199 = 51.99%

    Using the value of y we get,

    X = 1-y = 1-51.99 = 0.4801 = 48.01%

    So, relative abundance of two isotopes of europium are 151eu and 153eu are 48.01% and 51.99% respectively
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