Question

Gallium has an atomic mass of 69.723. The Ga-69 (68.926 amu) is 60.11%. What is the amu of the other isotope? I'd like to know the set up-thought it was (69.723)(0.6011) + (x)(0.3989)? But it isn't giving me the right answer.

Answer 1

`"70.924"`

The idea behind solving abundance or amu isotope problems is that each isotope contributes a fraction of its atomic mass - its abundance - to the average atomic mass.

#"(amu of isotope 1)" * "(fraction of isotope 1)" + "(amu of isotope 2)" * "(fraction of isotope 2)" = "(amu of mixture)" * 1.000#

So, in your particular case,

`68.926 * 0.6011 + x * (1 - 0.6011) = 69.723`

`x = (69.723 - 41.4311)/0.3989 = 70.924`

The set up you used is correct, since the abundance of the second gallium isotope is indeed equal to 1 - 0.6011 = 0.3989.

If you look up the actual atomic mass of `""^71Ga`, the second stable isotope of gallium, it's listed at 70.9247 amu, the exact same result you'd get using this set up, so I'm not sure why you didn't get the right answer.

Finally, the result makes sense because the average atomic mass of gallium is closer to the lighter isotope, `""^69Ga`, than it is to the heavier one, `""^71Ga`, so a 60-40 split between the two matches this difference.