The average atomic mass of a sample of an element X is 16.2 `mu`. What is the percentage of each isotope `overset(18)underset(8)X` and `overset(18)underset(8)X` in the sample?

Explanation

Let the % of isotope 15X = x and % of isotope `""_(8)^(18)X = 100 - x` Average atomic mass of an element (X) = 16.2 Average atomic mass
` = (" Mass of "_(8)^(18)X xx "percentange of "_(8)^(18)X )/(100)`
` or 16.2 =(x xx 16 +(100 -x) xx 18)/( 100 )`
` or 16.2 = ( 16 x + 1800 - 18 x )/(100)`
` or 1620 = 16 x + 1800 - 18 x`
` or 1620 = - 2x + 1800 or 2 x = 1800 - 1620 `
`or 2 x = 180 `
` therefore x= (180 )/(2) = 90`
Thus % of isotope `""_(8)^(16) X = 90`% %
`% ` of isotope `""_(8)^(18)X= (100 -90) = 10 %`