A sample of an element X contains two isotopes `._(8)^(16)X and ._(8)^(18)X`. If the average atomic mass of this sample of the element be 16.2 u, calculate the percentage of the two isotopes in this sample.

Explanation

In order to solve this problem, we will have to suppose that the percentage of one of the isotopes in the sample is x, so that the percentage of the other isotope in the sample will be (100 - x). Now :
(i) The mass of `._(8)^(16)X` isotope is 16 u. Suppose its percentage in the sample is x %
(ii) The mass of `._(8)^(18)X` isotope is 18 u. Its percentage in the sample will be (100 - x) %
So, Average atomic mass of `X = 16 xx (x)/(100) + 18 xx ((100 -x))/(100)`
But the avergae atomic mass of X has been given to be 16.2 u. Therefore,
`16.2=16xx(x)/(100)+18xx((100-x))/(100)`
or `16.2=(16x+1800-18x)/(100)`
or `16.2xx100=1800-2x`
or `2x=1800-1620`
or `2x=180`
And `x = (180)/(2)`
or `x =90`
Thus, the percentage of the isotope `._(8)^(16)X` in the sample is 90 %. The percentage of the other isotope `._(8)^(18)X` in the sample will be `100 - 90 = 10 %`.