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the atomic weight of a newly discovered element is 10.600 amu. it has two naturally occuring isotopes. one has a mass of 10.000 and a natural abundance of 70.000%. what is the isotopic mass of the other isotope?

Respuesta :

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[tex]10,6=\frac{10*70\%+x*30\%}{100\%}\\\\ 10,6=10*0,7+0,3x\\ 10,6-7=0,3x\\ 3,6=0,3x \\ x=12[/tex]

Answer: The isotopic mass of other isotope is 12 amu.

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]

Let the mass of isotope 2 be 'x' amu

  • For isotope 1:

Mass of isotope 1 = 10.000 amu

Percentage abundance of isotope 1 = 70 %

Fractional abundance of isotope 1 = 0.70

  • For isotope 2:

Mass of isotope 2 = x

Percentage abundance of isotope 2 = (100 - 70) % = 30 %

Fractional abundance of isotope 2 = 0.30

Average atomic mass of element = 10.600 amu

Putting values in above equation, we get:

[tex]10.600=[(10.000\times 0.70)+(x\times 0.3)]\\\\x=12[/tex]

Hence, the isotopic mass of other isotope is 12 amu.

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