Name: Composition of Nucleus
Uploaded: 2019-07-19
Duration: 1 min 54 s
Description: The atomic nucleus is the small, dense region of protons and neutrons at the centre of an atom. Here we will study the composition of the nucleus.

Question

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 ${}_{12}^{24}{Mg} (23.98504 u)$ , ${}_{12}^{25}{Mg} (24.98584 u)$ and ${}_{12}^{26}{Mg} (25.98259 u)$ . The natural abundance of ${}_{12}^{24}{Mg}$ is $78.99 %$ by mass. Calculate the abundances of other two isotopes.

Accepted Answer

The average atomic mass of magnesium, $m = 24.312 u$
Mass of magnesium ${}_{12}^{24}{M g}$ isotope, $m_{1} = 23.98504 u$
Mass of magnesium ${}_{12}^{25}{M g}$ , isotope, $m_{2} = 24.98584 u$
Mass of magnesium ${}_{12}^{26}{M g}$ isotope, $m_{3} = 25.98259 u$
Abundance of ${}_{12}^{24}{M g}$ , $η_{1} = 78.99 %$
Let the abundance of ${}_{12}^{25}{M g}$ , $η_{2} = x %$
Therefore, the abundance of ${}_{12}^{26}{M g}$ , $η_{3} = (100 - x - 78.99) = (21.01 - x) %$
We have the relation for the average atomic mass as:
$m = \frac{m_{1} η_{1} + m_{2} η_{2} + m_{3} η_{3}}{η_{1} {+ η}_{2} + η_{3}}$
$24.312 = \frac{23.98504 \times 78.99 + 24.98584 \times x + 25.98259 \times (21.01 - x)}{78.99 + x + (21.01 - x)}$
$0.99675 x = 9.2725255$
Hence, $x = 9.3 % = η_{2}$
${A n d η}_{3} = (21.01 - x) % = 11.71 %$
We can say that the abundance of ${}_{12}^{25}{M g}$ is $9.3 %$ and that of ${}_{12}^{26}{M g}$ is $11.71 %$ .

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