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An element X with a relative atomic mass of 210.2 has two isotopes, X-210 and X-212. What is the relative abundance of each isotope?

A. X-210: 10%, X-212: 90%
B. X-210: 20%, X-212: 80%
C. X-210: 30%, X-212: 70%
D. X-210: 40%, X-212: 60%

Answer :

Final answer:

The element X with an atomic mass of 210.2 and isotopes X-210 and X-212 has a relative abundance of approximately 70% for X-210 and 30% for X-212, so the correct answer is c) X-210: 30%, X-212: 70%.

Explanation:

The subject of this question is the calculation of the relative abundance of each isotope for an element X with an atomic mass of 210.2 and two isotopes, X-210 and X-212. The average atomic mass of an element is determined by the relative abundance and mass of its isotopes. Thus, we can set up the following equation where the percentages of the isotopes are represented as decimals (a and 1-a):

a*(210) + (1-a)*(212) = 210.2

By solving this equation, we find 'a', the relative abundance of the X-210 isotope, to be approximately 0.70 or 70%, and consequently, the relative abundance of the X-212 isotope is approximately 0.30 or 30%. Therefore, the answer is option c) X-210: 30%, X-212: 70%.

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