Calculating percent abundance?

Question

Gallium has two naturally-occuring isotopes 69-Gallium and 71-Gallium, with masses of 68.2957 amu and 70.9249 amu, respectively. How do I calculate the percent abundance of these two isotopes of gallium?

Answer 1

You look up the accurate Ar of Ga, and then:

(68.2957 y) + (70.9249 z)/(y + z) = Ar

Answer 2

Here's the "real" answer (just for fun). You plug into your model of the big bang, the expansion of the universe, the creation of our galaxy the age and composition of the Sun and the age and distance from the Sun of Earth. You'd probably need a supercomputer and a couple of hundred years to do the calculation. Ok, enuff fun For any TWO isotopes the atomic weight will be determined by: A1W1 + A2W2 = At.Wt. (where A1+A2 = 1 --the fractional abundances) In this example you'd know the atomic mass of isotope 1 ( = W1 ) and 2 ( = W2). This means you have two unknowns and two equations (i.e. A1 & A2) easy as π. For more than two isotopes the equations are similar At.Wt. = A1W1 + A2W2 +A3W3+...+AnWn (for n isotopes) and A1+A2+A3+...+An = 1 Problem is you now have more than two unknowns and only two equations. can't solve without more information. One additional "orthogonal" piece of information for each isotope after the first two. Experimental data of some sort, as far as I can see (until our models of the Universe become good enuff to really be useable - don't hold your breathe)