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**Average Atomic Mass** | Introduction to Chemistry

**Calculate** the **average atomic mass** of an **element** given its **isotopes** and their
natural ... An **element** can have differing numbers of neutrons in its **nucleus**, but it
... masses of the **element's isotopes**, each multiplied **by** its natural **abundance** on
Earth. ... To **calculate** the average **mass**, first convert the **percentages** into
fractions ...

For more information, see **Average Atomic Mass** | Introduction to Chemistry

Average atomic mass =\frac{\Sigma\text{isotope abundance * isotope mass }}{\Sigma\text{ isotope abundance }}

= \frac{\Sigma (m_i \eta_i)}{\Sigma \eta_i}

Step 1: Calculating the isotopes abundances

Given that

Average atomic mass magnesium = 24.313 u

Mass of ^{24}_{12} Mg = 23.98504 u

Mass of ^{25}_{12} Mg = 24.98584 u

Mass of ^{26}_{12} Mg = 25.98259 u

Abundance of ^{24}_{12} Mg = 78.99 %

Abundance of ^{25}_{12} Mg = x%

Abundance of ^{26}_{12} Mg = y% = 78.99 % + x% + y%= 100%

y% = 100% - 78.99 % - x% = 21.01% - x%

Substituting the all the values in the average atomic mass formula.

Average atomic mass = \frac{(23.98504 * 78.99) + (24.98584 * x) +(25.98259 * (21.01 - x))}{78.99 + x + 21.01 - x }

24.313 = \frac{(23.98504 * 78.99) + (24.98584 * x) +(25.98259 * (21.01 - x))}{100}

24.313 = \frac{1894.578 + 545.894 + x(24.98584 - 25.98259)}{100}

x = \frac{2440.472 - 2431.2}{0.99675}

x = 9.30

Abundance of ^{26}_{12} Mg = 21.01 - x = 21.01 - 9.30 = 11.71

Hence, Abundance of ^{25}_{12} Mg is 9.30% and Abundance of ^{26}_{12} Mg is 11.71%