An element $X$ has two naturally occurring isotopes with mass numbers 63 and 65. If the average atom

Question

An element $X$ has two naturally occurring isotopes with mass numbers 63 and 65. If the average atomic mass of element $X$ is exactly 63.6, the ratio of the natural abundance of the lighter isotope to the heavier isotope is

Professor PC Thomas Classes · Answer

(a) : Let the percentage abundance of the lighter isotope (${}^{63}X$) be $x$. Then, the abundance of the heavier isotope (${}^{65}X$) is $(100 - x)$. The average atomic mass is given by $\frac{63x + 65(100 - x)}{100} = 63.6$. This simplifies to $63x + 6500 - 65x = 6360 \implies 2x = 140 \implies x = 70$. Thus, the lighter isotope is $70\%$ abundant and the heavier is $30\%$ abundant. The ratio is $70:30$, which simplifies to $7:3$.