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NCERT Class XII Chapter
Nuclei
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Question : 23 of 31
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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. The three isotopes and their masses are  1224Mg\,\mathrm{^{24}_{12}Mg} (23.98504u),  1225Mg\,\mathrm{^{25}_{12}Mg} (24.98584 u) and  1226Mg\,\mathrm{^{26}_{12}Mg} (25.98259u). The natural abundance of  1224Mg\,\mathrm{^{24}_{12}Mg} is 78.99% by mass.
Calculate the abundances of the other two isotopes.
Solution:  
Let the abundance of isotope  1226Mg\,\mathrm{^{26}_{12}Mg} is x%, then the abundance of isotope  1225Mg\,\mathrm{^{25}_{12}Mg} is [100 – (x + 78.99)]%.
Average atomic mass of Mg 24.312 =
78.99×23.98504+[100−(x+78.99)]24.98584+x[25.98259]100\frac{78.99 \times 23.98504 + [100 - (x + 78.99)] 24.98584 + x[25.98259]}{100}
24.312 = 1894.5783 + 2498.564 + 0.99675 x – 1973.6157
x = 11.67340.996875\frac{11.6734}{0.996875} = 11.71
so, x = 11.71%, thus the abundance of  1226Mg\,\mathrm{^{26}_{12}Mg} is 11.71% and of  1225Mg\,\mathrm{^{25}_{12}Mg} is 9.303%.
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