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An element X has three isotopes: X²⁰, X²¹, and X²². The mole percentage of X²⁰ is 90% and the average atomic mass of X is 20.18. Which of the following option(s) is/are correct?

1. Mole percentage of X²¹ = 8%
2. Mole percentage of X²¹ = 3%
3. Mole percentage of X²² = 8%
4. Mole percentage of X²² = 2%

Correct answer: Mole percentage of X²¹ = 3%

Solution

Let %X²¹ = p and %X²² = q. Then p + q = 10 (since %X²⁰ = 90). Average mass: (90*20 + 21*p + 22*q)/100 = 20.18. So 1800 + 21p + 22q = 2018. Thus 21p + 22q = 218. From p + q = 10: q = 10 - p. So 21p + 22(10-p) = 218. 21p + 220 - 22p = 218. -p = -2. p = 2, but wait: let me recompute. Actually 21p + 220 - 22p = 218 gives -p = -2, so p = 2? No: 218 - 220 = -2, and -p = -2, so p = 2. Then q = 10 - 2 = 8. So %X²¹ = 2% and %X²² = 8%. Hmm, but option says X²¹ = 3% or 8%. Let me recheck: p = 2, q = 8 means %X²¹ = 2% and %X²² = 8%. But 2% for X²¹ is not an option... wait the options are: X²¹=8%, X²¹=3%, X²²=8%, X²²=2%. So correct is %X²² = 8% (option C). Let me reconfirm: 90*20 + 2*21 + 8*22 = 1800 + 42 + 176 = 2018. Average = 2018/100 = 20.18. Yes, correct. So %X²¹ = 2% and %X²² = 8%. Options C (X²² = 8%) is correct.

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