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Answer :
Final answer:
The natural abundance of Gallium-69 is 60.15%, and that of Gallium-71 is 39.85%, hence the correct answer is A. Gallium-69: 60.15%, Gallium-71: 39.85%.
Explanation:
To calculate the natural abundance of gallium isotopes, we can set up an equation using the given information. The atomic mass of Gallium-69 is 69.00014 and that of Gallium-71 is 70.9994. However, the example provided gives a different atomic mass for these isotopes (68.926 amu for Gallium-69 and 70.926 amu for Gallium-71) and an average atomic mass for gallium, which is 69.723 amu. To solve for the abundances, we denote the fractional abundance of Gallium-69 as 'x' and that of Gallium-71 as '1 - x'.
Using the equation:
69.723 amu = (x)(68.926 amu) + (1 - x)(70.926 amu)
We isolate 'x':
x(68.926 amu - 70.926 amu) = 69.723 amu - 70.926 amu
x(-2.000 amu) = -1.203 amu
x = 0.6015 or 60.15%
The fractional abundance of Gallium-71 is therefore 1 - x = 0.3985 or 39.85%.
Thus, the percent abundances for gallium's isotopes are 60.15% for Gallium-69 and 39.85% for Gallium-71, which corresponds to option A.
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