Question

Lithium exists in nature in the form of two isotopes, Li$ - 6$ and Li$ - 7$ with atomic masses $6.0151\,{\text{u}}$ and$7.0160\,{\text{u}}$ and the percentage $8.24$ and $91.76$ respectively. Calculate average atomic mass.

Answer 1

Hint: An element exists in diffident isotopes. The chemical elements that have a different number of neutrons are known as isotopes. The average mass of all isotopes is known as the average atomic mass of the element. The average atomic mass is determined by adding the product of the mass of each isotope and its percentages.

Formula used: \[{\text{Average}}\,{\text{atomic}}\,{\text{mass}}\,{\text{ = }}\,\sum {{\text{isotope}}\,{\text{mass}}\,{ \times }\,{\text{percent}}} {\text{ of that isotope}}\]

Complete answer:
The average atomic mass is the sum of the product of the mass of isotope and its percentages.

The formula of the average atomic mass is as follows:
\[{\text{Average}}\,{\text{atomic}}\,{\text{mass}}\,{\text{ = }}\,\sum {{\text{isotope}}\,{\text{mass}}\,{\times }\,{\text{percent}}} {\text{ of that isotope}}\]

For two isotopes of the lithium the formula can be written as follows:
${\text{Average}}\,{\text{atomic}}\,{\text{mass}}\,{\text{ = }}\,\,\left( {{\text{mass}}\,{\text{of}}{\,_6}{\text{Li}}\,\, \times \,\,{\text{percent}}\,{\text{of}}{{\text{ }}_6}{\text{Li}}\,\,} \right) + \left( {{\text{mass}}\,{\text{of}}{\,_7}{\text{Li}}\,\,\, \times \,\,{\text{percent}}\,{\text{of}}{{\text{ }}_7}{\text{Li}}\,\,} \right)\,$
Substitute $6.0151\,{\text{u}} $ for mass of $_6{\text{Li}}\,$, $8.24$% for percentage of $_6{\text{Li}}\,$, $7.0160\,{\text{u}}$ for mass of $_7 {\text{Li}}\, $ and $9 1.76 $% for percentage of $_7{\text{Li}}\,$
${\text{Average}}\,\,{\text{atomic}}\,\,{\text{mass}}\,\,{\text{of}}\,\,{\text{Li}}\,{\text{ = }}\,\,\left( {6.0151\,\, \times \,\,0.0824\,\,} \right) + \left( {7.0160\,\, \times \,\,0.9176\,\,} \right)\,$
${\text{Average}}\,\,{\text{atomic}}\,\,{\text{mass}}\,\,{\text{of}}\,\,{\text{Li}}\,\,{\text{ = }}\,\,\left( {0.4956} \right) + \left( {6.4379} \right)\,$
${\text{Average}}\,\,{\text{atomic}}\,\,{\text{mass}}\,\,{\text{of}}\,\,{\text{Li}}\,\,{\text{ = }}\,\,6.9335$

Therefore, the average atomic mass of lithium is $6.9335$.

Note:The percentages of isotopes represent the naturally occurring amount of the isotope that is the abundance. The total percentage abundance of all the isotopes of an element is considered as $100$%. So, if the percentage of one isotope is A, then the percentages of the second isotope will be $100 - {\text{A}}$ . So, we can determine the percentage of both isotopes of an element. The isotopes have the same number of the proton but different mass numbers due to different neutron numbers. Due to the same proton number, isotopes represent the same element.