Question

Which of the following is the closest to the observed abundance of 71Ga, one of two stable gallium isotopes (69Ga and 71Ga). The answer in the book shows 40%, and I have absolutely no idea how to solve this. Please help!

Answer 1

You must see the mass of Gallium in the periodic table. The mass present there is calculated by a weighted average of the mass of the isotopes, where the weights are the abundances of each isotope. Let X the isotopic abundance of Ga⁷¹. Since there are only Ga⁶⁹ and Ga⁷¹, the isotopic abundance of Ga⁶⁹ is 1-X. Then:

$m(Ga)_{periodic~table}=(1-X)\cdot m(Ga^{69})+X\cdot m(Ga^{71})\\\\69.7=(1-X)\cdot69+X\cdot71\\\\ 69.723=69-69X+71X\\\\ 2X=0.723\\\\ X=0.3615\\\\ \boxed{X=36.15\%}$

I don't know the options, but probably 40% is the closest to 36.15%.