To determine which pie chart best represents the relative abundances of the two isotopes of gallium ($\ce{Ga-69}$ and $\ce{Ga-71}$), we need to understand the concept of average atomic mass.

The average atomic mass of an element is calculated based on the relative abundances of its isotopes. For gallium, the average atomic mass is $\pu{69.72 u}$. This value is closer to the atomic mass of $\ce{Ga-69}$ (which is $\pu{68.9256 u}$) than to $\ce{Ga-71}$ (which is $\pu{70.9247 u}$). This suggests that $\ce{Ga-69}$ is more abundant than $\ce{Ga-71}$.

Given this information:

• Choice A shows $\ce{Ga-69}$ as less abundant, which would not result in an average atomic mass closer to 69.
• Choice B shows equal abundances, which would result in an average atomic mass closer to the midpoint between the two isotopes' masses, around $\pu{69.925 u}$.
• Choice C shows $\ce{Ga-69}$ as more abundant, which aligns with the average atomic mass of $\pu{69.72 u}$.

Therefore, the correct answer is Choice C. The part labeled $\ce{Ga-69}$ should be larger than the part labeled $\ce{Ga-71}$, reflecting that $\ce{Ga-69}$ is more abundant in nature.

Would you like to discuss the details further or have any other questions?

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Here are 5 related questions you might find interesting:

1. How is the average atomic mass of an element calculated using isotope abundances?
2. What are the exact masses of $\ce{Ga-69}$ and $\ce{Ga-71}$, and how do they contribute to the average atomic mass?
3. How do natural isotopic abundances vary among different elements?
4. What other methods besides pie charts can represent isotopic abundances?
5. Why are certain isotopes more abundant in nature than others?

Tip: Remember, when calculating the average atomic mass, isotopes with a mass closer to the average have a greater abundance.