Answer : The percent abundance of Li isotope-1 and Li isotope-2 is, 6.94 % and 93.1 % respectively.
Explanation :
Average atomic mass of an element is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.
Formula used to calculate average atomic mass follows:
[tex]\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i[/tex] .....(1)
Let the fractional abundance of Li isotope-1 be 'x' and the fractional abundance of Li isotope-2 will be '100-x'
For Li isotope-1 :
Mass of Li isotope-1 = 6.01512 amu
Fractional abundance of Li isotope-1 = x
For Li isotope-2 :
Mass of Li isotope-2 = 7.01600 amu
Fractional abundance of Li isotope-2 = 100-x
Average atomic mass of Li = 6.941 amu
Putting values in equation 1, we get:
[tex]6.941=[(6.01512\times x)+(7.01600\times (100-x))][/tex]
By solving the term 'x', we get:
[tex]x=694.048[/tex]
Percent abundance of Li isotope-1 = [tex]\frac{694.048}{100}=6.94\%[/tex]
Percent abundance of Li isotope-2 = 100 - x = 100-6.94 = 93.1 %
The relative abundance of the isotopes are 7.5% and 92.5%.
The relative atomic mass of an atom is the sum of the products of the relative atomic masses of its isotopes and their respective percentage abundance. We have been told in the question that the relative atomic mass of Li is 6.941 amu. Let the percentage abundance be x and 1-x
6.941 = 6.01512x + 7.01600(1 - x)
6.941 = 6.01512x + 7.01600 - 7.01600x
6.941 - 7.01600 = -1.00088x
-0.075 = -1.00088x
x = -0.075/-1.00088
x = 0.075
Hence, the other isotope is 1 - 0.075 = 0.925
Therefore, the relative abundance of the isotopes is 7.5% and 92.5%
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