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Naturally occurring carbon contains two isotopes of ${ }^{12} C$ and ${ }^{13} C$, the nuclidic masses of which are $12.0000$ and 13.0034. What is the percentage of the two isotopes in a sample of carbon whose atomic mass is 12.0111?

SOLUTION : Suppose the percentage of ${ }^{12} C$ isotope of mass $12 \cdot 0000=x$ and

hence that of ${ }^{13} C$ isotope of mass $13.0034=(100-x)$

$\text { Atomic mass of carbon }=\frac{x \times 12 \cdot 0+(100-x) \times 13 \cdot 0034}{100}$

$\therefore 12 \cdot 0111=\frac{12 x+1300 \cdot 34-13 \cdot 0034 x}{100}$

$\text { or, } \quad 1201 \cdot 11=-1 \cdot 0034 x+1300 \cdot 34,1 \cdot 0034 x=1300 \cdot 34-1201 \cdot 11 =99 \cdot 23$

$\therefore \therefore \text { and } \% \text { of isotope of mass } 13 \cdot 0034= 1 \cdot 1 0 6 \% .$

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