Question

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

$\begin{array}{ccc}\text{Isotope}& \text{Atomic Mass}& \text{Isotopic abundance}\\ {}^{24}Mg& 23.98504& 78.70\%\\ {}^{25}Mg& 24.98584& 10.13\%\\ {}^{26}Mg& 25.98259& 11.17\%\end{array}$

• A. 24.31
• B. 25.68
• C. 23.99
• D. 24.98

Answer 1

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 ${}^{24}Mg$ with atomic mass 23.98504 u, 10.13% of ${}^{25}Mg$ with atomic mass 24.98584 u and 11.17% of ${}^{26}Mg$ with atomic mass = 25.98259 u​.
Since,
Average atomic mass = ($M_1{P}_1$ + $M_2{P}_2$ + $M_3{P}_3$ +….) / 100​
where,
$M_1$=Atomic mass of isotope 1
​$P_1$=Percentage abundance of isotope 1​
$M_2$=Atomic mass of isotope 2​
$P_2$=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​