Question

Gallium has only two naturally occuring isotopes, Ga-69 and Ga-71. The mass of Ga-69 is 68.9256 amu, and the mass of Ga-70 is 70.9247 amu. Use the atomic mass of gallium to determine the relative abundace of each isotope in a naturally occuring sample.

Answer 1

You know what the isotopes each weigh, and you can easily look up the total. That sets up an equation that looks like:\[\%Ga_{69} * 68.9256amu + \%Ga_{71} * 70.9247amu = 69.72amu\] By itself that's 1 equation with 2 unknowns, but there's a second equation that links the 2 percentages.\[\%Ga_{69} + \%Ga_{71} = 100\%\]Since there's only 2 isotopes, the sum of their percentages umst equal 100%. Solve this equation for either percentage, then plug it into the first equation to solve for the remaining percentage.

Once you've found the first percentage, the other must be large enough to make up the difference from 100%.