The average atomic mass of a sample of an element X is 16.2 u.

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 ¹⁶₈ X isotope is 16u. Suppose its percentage in the sample is x%.

(ii) The mass of ¹⁸₈X isotope is 18 u. Its percentage in the sample will be (100-x)%.

So, Average atomic mass of X = 16 x X/100 + 18 x (100-x)/100

But the average atomic mass of X has been given to be 16.2 u. Therefore,

16.2 =16 x x/100 + 18 x (100-x)/100

16.2 = 16x + 1800 - 18x/100

16.2 ×100 = 1800-2x

2x = 1800 – 1620

2x = 180

x = 180/2

X = 90

Thus, the percentage of the isotope ¹⁶₈X in the sample is 90%. The percentage of the isotope ¹⁸₈X in the sample will be 100 – 90 = 10%.