Boron occurs in nature in the form of two isotopes having mass $$10$$ and $$11$$. Calculate the percentage abundances of $$B11$$ isotopes in a sample of boron having average atomic mass $$10.8$$.

Question

Boron occurs in nature in the form of two isotopes having mass $$10$$ and $$11$$. Calculate the percentage abundances of $$B11$$ isotopes in a sample of boron having average atomic mass $$10.8$$.

Infinity Learn · Accepted Answer

Isotopes of boron $$=10$$ B and  $$11$$ B. Let, total number of moles of $$=10$$ B and  $$11B=1Let$$ fractional abundance of  $$10B=$$α;Fractional abundance of  $$11B=1$$−αBut, average atomic mass $$=$$ [Fractional abundance of $$10B$$× mass of $$10B+$$[Fractional abundance of  $$11B$$× mass of  $$11B.10.8=($$α×$$10)+(1$$−α$$)$$×$$11=10$$α$$+11$$−$$11$$αor, α$$=11$$−$$10.8$$;α$$=0.2$$ Hence $$1$$−α$$=1$$−$$0.2=0.8$$∴ % age abundance of  $$10B$$                                  $$=$$ $$0.2$$ X $$100$$ $$=$$ $$20$$%    % age abundance of  $$11B$$                                  $$=$$ $$0.8$$ X $$100$$ $$=$$ $$80$$%.

Boron occurs in nature in the form of two isotopes having mass 10 and 11. Calculate the percentage abundances of B11 isotopes in a sample of boron having average atomic mass 10.8.

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