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In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. - Physics

Numerical

In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are\[\ce{_12^24Mg}\](23.98504 u), \[\ce{_12^25Mg}\] (24.98584 u), and \[\ce{_12^26Mg}\] (25.98259 u). The natural abundance of \[\ce{_12^24Mg}\] is 78.99% by mass. Calculate the abundances of other two isotopes.

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Solution

Data: Average atomic mass of magnesium = 24.312 u, \[\ce{_12^24Mg}\] : 23.98504 u, \[\ce{_12^25Mg}\] : 24.98584 u, \[\ce{_12^26Mg}\] : 25.98259 u, \[\ce{_12^24Mg}\] : 78.99% by mass

∴ `24.312 = ((23.98504)(78.99) + (24.98584)"x" + (25.98259)(100 - 78.99 - "x"))/100`

∴ `24.312 = 18.9457831 + (24.98584"x")/100 + 25.98259 - 20.52364784 - (25.98259"x")/100`

∴ `(0.99675)/100 "x" = 0.09272526`

∴ x = 9.30 %

100 - 78.99 - 9.30 = 11.71

∴ \[\ce{_12^25Mg}\] : 9.30 % be mass and \[\ce{_12^26Mg}\] : 11.71 % by mass

Concept: Mass-energy and Nuclear Binding Energy - Nuclear Binding Energy
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Balbharati Physics 12th Standard HSC Maharashtra State Board
Chapter 15 Structure of Atoms and Nuclei
Exercises | Q 24 | Page 343
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