The average atomic mass of a sample of an element X is 16.2 u. What are the percentages of isotopes `._(8)^(16)X` and `._(8)^(18)X` in the sample.

Explanation

It is given that the average atomic mas of the sample of element X is 16.2. Let the percentage of isotope `._(8)^(18)X` be Y%. Thus the percentage of isotope `._(8)^(16)X` will be `(100-Y)%` therefore
`18xx(y)/(100)+16xx((100-y))/(100)=16.2`
`(18y)/(100)+(16(100-y))/(100)=16.2`
`(18y+1600-16y)/(100)=16.2`
`18Y+1600-16Y=1620`
`2Y+1600=1620`
`2Y=1620-1600`
`-Y=10`
Therefore the percentage of isotope of `._(8)^(18)X` is 10 %
And the percentage of isotope `._(8)^(16)X` is `(100-10)%=90%`.