Question

The average atomic mass of two isotopes with mass numbers A and A + 2 is A + 0.25. Calculate the percentage abundance of the isotopes.

Answer 1

$$\begin{gathered} Averageatomicmass=\frac{x_1{M}_1+x_2{M}_2}{x_1+x_2} \\ Where{x}_{1}and{x}_{2}arethe\%abundance. \\ {M}_{1}and{M}_{2}arethemolarmass \\ {x}_1+x_2=100\% \\ {x}_2=100-x_1 \\ Averageatomicmass=\frac{x_1{M}_1+x_2{M}_2}{x_1+x_2} \\ A+0.25=\frac{x_1\times A+(100-x_1)(A+2)}{100} \\ 100A+25=A{x}_1+100A+200-A{x}_1-2x_1 \\ 2x_1=200-25=175 \\ {x}_1=\frac{175}{2}=87.5\% \\ {x}_2=100-x_1=100-87.5=12.5\% \end{gathered}$$