Question

Determine the percent abundance of gallium-69?

There are only two isotopes of gallium: ^69Ga (68.926 amu) and ^71Ga(70.025 amu). The average atomic mass of gallium is 69.723 amu. What is the percent of abundance of gallium-69? Please show all calculations involved.

Answer 1

When you have 2 isotopes of an element, their weighted average must be equal to the mass on the PT. That sets up 2 equations\[69.723amu = (\%x)*(68.926amu) + (\%y)*(70.025amu)\] What's missing are the percentages x and y. The second equation comes from the fact that whatever the percentages are, they must add up to 100% of the sample (since there's nothing else around)\[\%x + \%y = 1\]
2 equations with 2 unknowns means rearrange and solve for either %x or %y. \[69.723amu = (\%x)*(68.926amu) + (1-\%x)*(70.025amu)\] Solve for %x.