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Q.

The average atomic mass of a sample of an element ‘X’ is 16.2 u. The percentage of each isotope

$_{8}^{16} X$ and $_{8}^{18} X$ in the sample is

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a

85 and 15 respectively

b

90 and 10 respectively

c

70 and 30 respectively

d

80 and 20 respectively

answer is A.

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Detailed Solution

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The average atomic mass of a sample of an element ‘X’ is 16.2 u. The percentage of each isotope

_{8}^{16} X

and

_{8}^{18} X

in the sample is 90 and 10 respectively.
Because its numerical value is equal to the element's molar mass, the average atomic mass is helpful. Because weighing is often the simplest method to quantify a substance, it is useful to know how much of a solid to take when you want to react it with some known quantity of another reagent.
Let the percentage of

_{8}^{16} X

be A.
Then the percentage of

_{8}^{18} X

be (100-X)%.

16 \times \frac{A}{100} + 18 \times \frac{(100 - A)}{100} = 16.2

\Rightarrow 1800 - 2 A = 1620

\Rightarrow A = 90 %

and 100 - A = 10 %

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