Math Problem Statement

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)   

Ga-69Ga-71

A

Ga-69Ga-71

(Choice B)   

Ga-69Ga-71

B

Ga-69Ga-71

(Choice C)   

Ga-69Ga-71

C

Solution

Given that gallium has two naturally occurring isotopes, \ceGa69\ce{Ga-69} and \ceGa71\ce{Ga-71}, with an average atomic mass of \pu69.72u\pu{69.72 u}, we can infer the relative abundances of these isotopes.

Since the average atomic mass (\pu69.72u\pu{69.72 u}) is closer to the atomic mass of \ceGa69\ce{Ga-69} (around \pu68.93u\pu{68.93 u}) than to \ceGa71\ce{Ga-71} (around \pu70.92u\pu{70.92 u}), it indicates that \ceGa69\ce{Ga-69} is more abundant than \ceGa71\ce{Ga-71}.

Therefore, the correct pie chart should show that \ceGa69\ce{Ga-69} has a larger portion compared to \ceGa71\ce{Ga-71}. The answer corresponds to:

Choice C - The pie chart where the segment representing \ceGa69\ce{Ga-69} is larger than that of \ceGa71\ce{Ga-71}.

Would you like further details or have any other questions?


Here are 5 related questions you might find interesting:

  1. How do isotopic abundances affect the calculation of average atomic mass?
  2. Why is the average atomic mass of gallium closer to \ceGa69\ce{Ga-69} than \ceGa71\ce{Ga-71}?
  3. What are the exact isotopic masses of \ceGa69\ce{Ga-69} and \ceGa71\ce{Ga-71}?
  4. How can you experimentally determine the relative abundances of isotopes?
  5. What is the significance of isotopic abundance in chemistry and material science?

Tip: When analyzing average atomic mass, the closer the average is to an isotope's mass, the more abundant that isotope is.

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Math Problem Analysis

Mathematical Concepts

Isotopes
Atomic Mass
Average Atomic Mass

Formulas

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Theorems

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Suitable Grade Level

High School