Question

Magnesium has three naturally occurring isotopes with masses of \[23.99{\text{ a}}{\text{.m}}{\text{.u}}\] , \[24.99{\text{ a}}{\text{.m}}{\text{.u}}\] , \[25.98{\text{ a}}{\text{.m}}{\text{.u}}\] and natural abundances of \[78.99{{ \% }}\] , \[10.00{{ \% }}\] and \[11.01{{ \% }}\] respectively. How do you calculate the atomic mass of magnesium?

Answer 1

Hint: Here we will have to find the atomic mass of magnesium with the given atomic masses of its isotopes. The atomic mass of an element is the average mass of its isotopes with its abundance percentage in nature. Thus we have to find the average mass of isotopes with their abundances in nature.

Complete answer:
Isotopes are those elements which have the same atomic number but have different mass numbers. For such an element which has its isotopes we calculate its average atomic mass. To find the average atomic mass we have to know about the isotopic mass of each isotope and its percentage of abundance in nature. According to question magnesium has three isotopes and abundance of each isotope is given as: \[23.99{\text{ a}}{\text{.m}}{\text{.u }}\left( {78.99{{ \% }}} \right)\], \[24.99{\text{ a}}{\text{.m}}{\text{.u }}\left( {10.00{{ \% }}} \right)\] and \[25.98{\text{ a}}{\text{.m}}{\text{.u }}\left( {11.01{{ \% }}} \right)\]. Hence the average atomic mass of magnesium can be written by using formula as:
Atomic mass of magnesium \[ = {\text{ }}\dfrac{{23.99{\text{ }} \times {\text{ }}78.99{\text{ + }}24.99{\text{ }} \times {\text{ 10}}{\text{.00 + }}25.98{\text{ }} \times {\text{ 11}}{\text{.01}}}}{{100}}\]
Atomic mass of magnesium \[ = {\text{ }}\dfrac{{23.99{\text{ }} \times {\text{ }}78.99{\text{ + }}24.99{\text{ }} \times {\text{ 10}}{\text{.00 + }}25.98{\text{ }} \times {\text{ 11}}{\text{.01}}}}{{100}}\]
Atomic mass of magnesium \[ = {\text{ }}\dfrac{{{\text{1894}}{\text{.28 + 249}}{\text{.9 + }}286.03}}{{100}}\]
Atomic mass of magnesium \[ = {\text{ 18}}{\text{.94 + 2}}{\text{.49 + 2}}{\text{.86}}\]
Atomic mass of magnesium \[ = {\text{ 24}}{\text{.29 a}}{\text{.m}}{\text{.u}}\]
Thus we take the atomic mass of magnesium as \[24{\text{ a}}{\text{.m}}{\text{.u}}\].

Note:
a.m.u here stands from atomic mass per unit. For one mole of magnesium it is taken in \[g{\text{ mo}}{{\text{l}}^{ - 1}}\]. The average atomic mass is the average of all isotopic masses of the compound, thus we use the average atomic mass of the element rather than taking individual atomic mass for different isotopes of the element. Abundance of element refers to the existence percentage of the isotope in nature. The average atomic mass is closer to that isotope which has a higher abundance percentage in nature.