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Question

What is the average atomic mass of Mg if the naturally occurring isotopes are 24Mg, 25Mg and 26Mg. Their masses and abundances are as follows:

IsotopeAtomic MassIsotopic abundance24Mg23.9850478.70%25Mg24.9858410.13%26Mg25.9825911.17%

A
24.31
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B
25.68
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C
23.99
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D
24.98
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Solution

The correct option is A 24.31
The relative abundance of an isotope is the percentage of atoms with a specific atomic mass found in a naturally occurring sample of an element.​ On adding the abundance percentage of the three isotopes we get the total abundance of magnesium, (78.70 + 10.13 + 11.17)% = 100% ​
This means that out of the total elemental magnesium (100%) , consists of 78.70% of 24Mg with atomic mass 23.98504 u, 10.13% of 25Mg with atomic mass 24.98584 u and 11.17% of 26Mg with atomic mass = 25.98259 u​.
Since,
Average atomic mass = (M1P1 + M2P2 + M3P3 +….) / 100​
where,
M1=Atomic mass of isotope 1
P1=Percentage abundance of isotope 1​
M2=Atomic mass of isotope 2​
P2=Percentage abundance of isotope 2

The average atomic mass of magnesium will be
​= (23.98504 x 78.70 + 24.98584 x 10.13 +25.95259 x 11.17)/100 ​
= 24.31 u​

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