https://file.aiquickdraw.com/mathbot/file/172611094780414fdpjdr.jpg

Use the mass spectrum of rubidium to determine the atomic mass of rubidium.


The image shows a mass spectrum of rubidium with two isotopes having masses of 85 amu and 87 amu, along with their respective intensities (abundances) as percentages. To determine the atomic mass of rubidium, we can calculate the weighted average based on the given abundances and isotopic masses.

### Step-by-step process:

1. **Extract the data from the spectrum:**
   - Isotope 1: Mass = 85 amu, Intensity = 100% (relative abundance).
   - Isotope 2: Mass = 87 amu, Intensity = approximately 27%.

2. **Convert the relative intensities to fractional abundances:**
   - For Isotope 1 (Rb-85): 100% = 1.00.
   - For Isotope 2 (Rb-87): 27% = 0.27.

3. **Find the total intensity (sum of abundances):**
   \[
   \text{Total intensity} = 1.00 + 0.27 = 1.27
   \]

4. **Calculate the fractional abundance of each isotope:**
   - Fractional abundance of Rb-85:
     \[
     \frac{1.00}{1.27} \approx 0.787
     \]
   - Fractional abundance of Rb-87:
     \[
     \frac{0.27}{1.27} \approx 0.213
     \]

5. **Calculate the atomic mass of rubidium:**
   Use the weighted average formula:
   \[
   \text{Atomic mass} = (0.787 \times 85) + (0.213 \times 87)
   \]
   \[
   \text{Atomic mass} \approx 66.895 + 18.531 = 85.426 \, \text{amu}
   \]

### Conclusion:
The atomic mass of rubidium, based on the given spectrum, is approximately **85.43 amu**.

Let me know if you need further details or have any questions!

### Related Questions:
1. What are isotopes, and how do they affect the atomic mass of an element?
2. Why is the atomic mass not a whole number?
3. How are mass spectrometry readings interpreted for other elements?
4. What would happen to the atomic mass if the intensity of the Rb-87 isotope increased?
5. How does rubidium's atomic mass compare with other alkali metals?

### Tip:
Mass spectrometry is a powerful tool in determining isotopic composition and relative atomic masses by measuring the abundance and mass of isotopes.

Use the mass spectrum of rubidium to determine the atomic mass of rubidium.

Learn how to calculate the atomic mass of rubidium using the mass spectrum data. The problem covers key concepts like isotopic masses and relative abundances. Suitable for high school students, grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation