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Explain which isotope of cerium is the most abundant?

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elahusb | Student, College Freshman | (Level 1) eNoter

Posted May 21, 2013 at 4:39 PM via web

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Explain which isotope of cerium is the most abundant?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 21, 2013 at 5:07 PM (Answer #1)

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The number of isotopes of Cerium is 8 but the isotopes `Ce^140` and `Ce^142` are present in considerable quantities, hence, you need to evaluate what is the most abundant isotope between `Ce^140` and `Ce^142` .

You need to consider the atomic mass of Ce from periodic table, such that:

Atomic mass `= 140.11`

You need to use the following relation to evaluate te most abundant isotope, such that:

`(1-x)*mass Ce^142 + x*mass Ce^140 = 140.11`

`(1-x)*142 + x*140 = 140.11`

`142 - 142x + 140x = 140.11`

`-2x = -1.89 => x = 1.89/2 = 0.945`

Hence, evaluating the most abundant isotope of Cerium, considering only the `Ce^140` and `Ce^142` isotopes, yields `Ce^140` is the most abundant isotope.

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