Question

Boron has only to naturally occurring isotopes. The mass of boron-10 is 10.01294 amu and the mass of bornon-11 is 11.00931 amu. Calculate the relative abundances of the two isotopes

Answer 1

In order to find the percentages, we need to know what the total is. The average mass of boron is 10.811amu. Whatever the percentages are, they have to add up to 100%. This allows us to make 2 linked equations:\[(\%_{B10} *10.01294amu) + (\%_{B11}*11.00931amu) = 10.811amu\]and\[\% _{B10} + \%_{B11} = 100\%\]

Rearrange the second equation to solve for either percentage. \[\%_{B10} = 100\% - \%_{B11}\]Then replace that in the first equation to solve for one of the percentages. \[((100\% - \%_{B11}) *10.01294amu) + (\%_{B11}*11.00931amu) = 10.811amu\]The other percentage has to add up to 100%.