Question

Boron exists in two isotopes, boron $ - 10 $ and boron $ - 11 $ . Based on the atomic mass, $ 10.81{\text{ }}amu $ ,which isotope should be more abundant?

Answer 1

Hint: Since it is given the isotopes of boron, thus we can find the percentage composition of each isotope by using the average atomic mass of the boron. The isotope having greater percentage of composition that isotope is more abundant. We will find the composition of each isotope by calculating average mass.

Complete Step By Step Answer:
We are given two isotopes of boron which are , boron $ - 10 $ and boron $ - 11 $ . Isotopes are those elements which have the same atomic number but different mass number. Thus we are also given the average atomic mass of boron as $ 10.81{\text{ }}amu $ . For finding the percentage composition of both isotopes in this average atomic mass we will assume the percentage composition of boron $ - 10 $ as $ x $ then the percentage composition of boron $ - 11 $ will be $ 100 - x $ . Thus the average atomic mass can be represented as:
 $ \Rightarrow \dfrac{{10{\text{ }} \times {\text{ }}x{\text{ }} + {\text{ }}\left( {100 - x} \right){\text{ }} \times {\text{ }}11}}{{100}}{\text{ }} = {\text{ }}10.81 $
On cross multiplication and solving we get,
 $ \Rightarrow 10x{\text{ }} + {\text{ }}\left( {100 - x} \right){\text{ }} \times {\text{ }}11{\text{ }} = {\text{ }}1081 $
 $ \Rightarrow {\text{x }} = {\text{ 1100 - }}1081 $
 $ \Rightarrow {\text{x }} = {\text{ 19}} $
Thus boron $ - 10 $ is only $ 19{\text{ \% }} $ and the rest is boron $ - 11 $ . Thus we can say that boron $ - 11 $ is more abundant than boron $ - 10 $ .

Note:
The average atomicity of boron $ - 10 $ and boron $ - 11 $ theoretically is $ 10.5 $ . But practically the average atomic mass of boron is $ 10.81{\text{ }}amu $ . Thus it shows that boron $ - 11 $ has greater abundance in the average atomic mass of boron. The atomic mass is measured in atomic mass per unit which is represented as $ amu $ . The atomic number of boron is five and it contains three valence electrons. Since the average atomic mass of boron is near to the atomic mass of boron $ - 11 $ isotope we can also predict that boron $ - 11 $ has greater abundance in nature.