Gallium has two naturally occurring isotopes,
\[\ce{Ga-69}\] and
\[\ce{Ga-71}\]. The average atomic mass of gallium is
\[\pu{69.72 u}\].
Which pie chart best shows the relative abundances of the two isotopes in nature?
Choose 1 answer:
Choose 1 answer:
(Choice A)   A pie chart is shown. It is divided into 2 unequal parts labeled gallium 69 and gallium 71. The part labeled gallium 69 is smaller than the part labeled gallium 71.

A
A pie chart is shown. It is divided into 2 unequal parts labeled gallium 69 and gallium 71. The part labeled gallium 69 is smaller than the part labeled gallium 71.
(Choice B)   A pie chart is shown. It is divided into 2 equal parts labeled gallium 69 and gallium 71.

B
A pie chart is shown. It is divided into 2 equal parts labeled gallium 69 and gallium 71.
(Choice C)   A pie chart is shown. It is divided into 2 unequal parts labeled gallium 69 and gallium 71. The part labeled gallium 69 is larger than the part labeled gallium 71.

C
A pie chart is shown. It is divided into 2 unequal parts labeled gallium 69 and gallium 71. The part labeled gallium 69 is larger than the part labeled gallium 71.

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.

Explore the concept of average atomic mass through the example of gallium isotopic abundances. Learn how isotopic ratios affect the calculation of average atomic mass, with a focus on Gallium-69 and Gallium-71. Suitable for advanced high school students and chemistry enthusiasts.

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