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Answers
Every chemical element has one or more radioactive isotopes. For example, hydrogen, the lightest element, has three isotopes with mass numbers 1, 2, and 3. Only hydrogen-3 (tritium), however, is a radioactive isotope, the other two being stable. More than 1,000 radioactive isotopes of the various elements are known.
Radioactive isotopes have many useful applications. In medicine, for example, cobalt-60 is extensively employed as a radiation source to arrest the development of cancer.
The percentage of one isotope is coming out to be 75% and the percentage of other isotope is coming out to be 25%.
Explanation:
It is given that, an element has 2 isotopes. Let the fractional abundance of first isotope be 'x', so the fractional abundance for another isotope will be '(1 - x)' because the total fractional abundance is always equal to 1.
For isotope 1, which is _{17}^{35}\textrm{Z}
17
35
Z :
Mass of this isotope = 35 u
Fractional abundance = x
For isotope 2, _{17}^{37}\textrm{Z}
17
37
Z :
Mass of this isotope = 37 u
Fractional abundance = 1 - x
Average atomic mass of element Z = 35.5 u
Expression for the average atomic mass of an element is given by the equation:
\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_iAverage atomic mass =∑
i=1
n
(Atomic mass of an isotopes)
i
×(Fractional abundance)
i
Putting values in above equation, we get:
\begin{lgathered}35.5=[(35\times x)+37(1-x)]\\\\1.5=2x\\\\x=0.75\end{lgathered}
35.5=[(35×x)+37(1−x)]
1.5=2x
x=0.75
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Every chemical element has one or more radioactive isotopes. For example, hydrogen, the lightest element, has three isotopes with mass numbers 1, 2, and 3. Only hydrogen-3 (tritium), however, is a radioactive isotope, the other two being stable. More than 1,000 radioactive isotopes of the various elements are known.
Radioactive isotopes have many useful applications. In medicine, for example, cobalt-60 is extensively employed as a radiation source to arrest the development of cancer.
The percentage of one isotope is coming out to be 75% and the percentage of other isotope is coming out to be 25%.
Explanation:
It is given that, an element has 2 isotopes. Let the fractional abundance of first isotope be 'x', so the fractional abundance for another isotope will be '(1 - x)' because the total fractional abundance is always equal to 1.
For isotope 1, which is _{17}^{35}\textrm{Z}
17
35
Z :
Mass of this isotope = 35 u
Fractional abundance = x
For isotope 2, _{17}^{37}\textrm{Z}
17
37
Z :
Mass of this isotope = 37 u
Fractional abundance = 1 - x
Average atomic mass of element Z = 35.5 u
Expression for the average atomic mass of an element is given by the equation:
\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_iAverage atomic mass =∑
i=1
n
(Atomic mass of an isotopes)
i
×(Fractional abundance)
i
Putting values in above equation, we get:
\begin{lgathered}35.5=[(35\times x)+37(1-x)]\\\\1.5=2x\\\\x=0.75\end{lgathered}
35.5=[(35×x)+37(1−x)]
1.5=2x
x=0.75
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