Question

An element X exist in two isotopic form with its atomic mass 10+11. If it’s average atomic mass is 10.6 , what will be the percentage of each isotope?

Answer 1

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Answer 2

The percentage abundance of isotope 1 be 40 % and isotope 2 be 60 %

Explanation:

Average atomic mass is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.

The equation used to calculate average atomic mass follows:

$\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i$

Let the fractional abundance of isotope 1 be 'x' and that of isotope 2 be '1-x'

• For isotope 1:

Mass of isotope 1 = 10 amu

Fractional abundance of isotope 1 = x

• For isotope 2:

Mass of isotope 2 = 11 amu

Fractional abundance of isotope 2 = (1 - x)

Average atomic mass of the atom = 10.6 amu

Putting values in above equation, we get:

$10.6=[(10\times x)+(11\times (1-x))]\\\\x=0.4$

Percentage abundance of isotope 1 = $0.4\times 100=40\%$

Percentage abundance of isotope 1 = $(1-x)=(1-0.4)=0.6\times 100=60\%$

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