The element bron occurs in nature as two isotopes havein atomic masses 10 u and 11 u . What are the percentage abundances of these isotopes in a sample of boron having average atomic mass of 10.8 u?

Explanation

Let the % abundance of `""^(10)B` isotope =x
Then, % abundance of `""^(11)B` isotope = 100 -x
The average atomic mass `=(x xx 10 + (100-x) xx 11)/100`
But, average atomic mass = 10.8
`therefore (x xx 10 + (100 -x) xx 11)/100 = 10.8`
or `10x + 1100 - 11 x = 10.8 xx 100`
`-x = -1100 + 1080`
or x=20
Thus, percentage abundance, `""^(10)B=20, ""^(11)B=80`