There are only two naturally-occuring stable isotopes of antimony, the masses of which are listed in the table below. Use whatever data you need from the ALEKS Periodic Table to calculate the natural abundance of each isotope and complete the table.

Be sure your answers have the correct number of significant digits.

isotope	mass
(amu)	natural abundance
 


To calculate the natural abundance of antimony's two naturally occurring isotopes, you will need to use their atomic masses and the average atomic mass of antimony (Sb) from the periodic table. The general method is as follows:

### Steps:

1. **Identify the isotopes of antimony**: Antimony has two naturally occurring isotopes:  
   - **\(^{121}\)Sb** (mass = 120.9038 amu)
   - **\(^{123}\)Sb** (mass = 122.9042 amu)
   
2. **Average atomic mass of antimony**: The average atomic mass of antimony from the periodic table is **121.760 amu** (based on current periodic tables).

3. **Let the natural abundance of \(^{121}\)Sb be \(x\), and the natural abundance of \(^{123}\)Sb be \(1 - x\)**. These abundances are expressed as fractions or percentages, which must sum to 1 (or 100%).

4. **Set up the equation based on the weighted average**:

   \[
   (\text{mass of }^{121}\text{Sb}) \cdot x + (\text{mass of }^{123}\text{Sb}) \cdot (1 - x) = \text{average atomic mass of Sb}
   \]
   
   Substituting the known values:

   \[
   120.9038x + 122.9042(1 - x) = 121.760
   \]

5. **Solve for \(x\)**:

   Distribute and simplify:

   \[
   120.9038x + 122.9042 - 122.9042x = 121.760
   \]

   Combine like terms:

   \[
   -2.0004x + 122.9042 = 121.760
   \]

   Isolate \(x\):

   \[
   -2.0004x = 121.760 - 122.9042
   \]

   \[
   -2.0004x = -1.1442
   \]

   Solve for \(x\):

   \[
   x = \frac{-1.1442}{-2.0004} = 0.5721
   \]

6. **Calculate the natural abundance of each isotope**:
   - \(x = 0.5721\), which means the natural abundance of \(^{121}\)Sb is **57.21%**.
   - The natural abundance of \(^{123}\)Sb is \(1 - 0.5721 = 0.4279\), or **42.79%**.

### Final Answer:
- \(^{121}\)Sb natural abundance = **57.21%**
- \(^{123}\)Sb natural abundance = **42.79%**

Would you like more details or explanations about this process? Here are some additional questions to expand the topic:

1. How do significant figures impact the calculation of isotope abundances?
2. What is the difference between stable and unstable isotopes?
3. Why do naturally occurring elements have isotopes?
4. How can mass spectrometry be used to determine isotope abundances?
5. What other elements have multiple naturally occurring isotopes?

**Tip**: Always check significant figures based on the input data (like atomic masses and percentages) to ensure precision in your calculations.

There are only two naturally-occuring stable isotopes of antimony, the masses of which are listed in the table below. Use whatever data you need from the ALEKS Periodic Table to calculate the natural abundance of each isotope and complete the table.

Be sure your answers have the correct number of significant digits.

Learn how to calculate the natural abundance of antimony's isotopes (121Sb and 123Sb) using their atomic masses and the average atomic mass from the periodic table. This detailed step-by-step solution covers key algebraic concepts and is suitable for high school students.

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