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To find the atomic mass of ruthenium for the environment on the planetesimal "98765 ALEKS," we can calculate the weighted average of the isotope masses based on their relative abundances. Here’s the approach:

1. **Use the Formula for Weighted Average**:
   \[
   \text{Atomic Mass} = (m_1 \times a_1) + (m_2 \times a_2)
   \]
   where \( m_1 \) and \( m_2 \) are the masses of the isotopes, and \( a_1 \) and \( a_2 \) are their relative abundances (converted to decimal form).

2. **Values from the Table**:
   - **For \( ^{99}\text{Ru} \)**: Mass = 98.91 amu, Relative Abundance = 93.9% = 0.939
   - **For \( ^{100}\text{Ru} \)**: Mass = 99.90 amu, Relative Abundance = 6.1% = 0.061

3. **Calculate the Atomic Mass**:
   \[
   \text{Atomic Mass} = (98.91 \times 0.939) + (99.90 \times 0.061)
   \]

4. **Solve**:
   - For \( ^{99}\text{Ru} \): \( 98.91 \times 0.939 = 92.81829 \)
   - For \( ^{100}\text{Ru} \): \( 99.90 \times 0.061 = 6.0939 \)
   - Add these together:
     \[
     92.81829 + 6.0939 = 98.91219
     \]

5. **Round to Significant Digits**:
   Since the values provided are to four significant figures, the atomic mass should also be rounded to four significant figures:
   \[
   \text{Atomic Mass} \approx 98.91 \, \text{amu}
   \]

**Final Answer**: The atomic mass of ruthenium on "98765 ALEKS" is **98.91 amu**.

Would you like further clarification or details?

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Here are some related questions to expand your understanding:

1. What role do isotopes play in determining atomic mass?
2. How is relative abundance used in calculating atomic masses?
3. Why is the atomic mass on Earth potentially different from other locations?
4. What is the significance of significant figures in scientific calculations?
5. How does this approach differ for elements with multiple isotopes?

**Tip**: Always remember to convert percentages into decimal form when using them in calculations.

A robot spacecraft returned samples from the planetesimal 98765 ALEKS, located in the outer Solar System. Mass-spectroscopic analysis produced the following data on the isotopes of ruthenium in these samples:

- Isotope 99Ru: Mass = 98.91 amu, Relative Abundance = 93.9%
- Isotope 100Ru: Mass = 99.90 amu, Relative Abundance = 6.1%

Use these measurements to complete the entry for ruthenium in the Periodic Table that would be used on 98765 ALEKS.

Learn how to calculate the atomic mass of ruthenium on the planetesimal 98765 ALEKS using isotopic masses and relative abundances. This problem covers key concepts in chemistry, including the weighted average formula and significant figures. Suitable for students in Grades 9-12.

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