Gallium (Ga) consists of two naturally occurring isotopes with masses of 68.926 and 70.925 u. The average atomic mass of Ga is 69.72 u. Calc

Let f1 be the fraction of isotope 1 and f2 be the fraction of isotope 2.  Then:

 

f1 + f2 = 1

 

68.926*f1 + 70.925*f2 = 69.72

 

Replace f2 in the second equation using the fact that f2 = 1 - f1 from the first equation and solve for f1:

 

$${\mathtt{68.926}}{\mathtt{\,\times\,}}{\mathtt{f1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{70.925}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{f1}}\right) = {\mathtt{69.72}} \Rightarrow {\mathtt{f1}} = {\frac{{\mathtt{1\,205}}}{{\mathtt{1\,999}}}} \Rightarrow {\mathtt{f1}} = {\mathtt{0.602\: \!801\: \!400\: \!700\: \!350\: \!2}}$$

 

So f1 ≈ 0.603 and f2 ≈ 1 - 0.603 = 0.397

 

or f1 ≈ 60.3% and f2 ≈ 39.7%

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