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To find the entry for ruthenium based on the isotopic data provided, we need to calculate the average atomic mass using the masses and relative abundances of each isotope. The formula for calculating the weighted average atomic mass is:

\[
\text{Average Atomic Mass} = (\text{mass of isotope}_1 \times \text{relative abundance}_1) + (\text{mass of isotope}_2 \times \text{relative abundance}_2)
\]

The data given is:
- For \( \text{Ru}^{102} \): mass = 101.90 amu, relative abundance = 92.2% (or 0.922 as a decimal)
- For \( \text{Ru}^{100} \): mass = 99.90 amu, relative abundance = 7.8% (or 0.078 as a decimal)

### Step-by-Step Calculation

1. Convert the percentages to decimals:
   - \( 92.2\% = 0.922 \)
   - \( 7.8\% = 0.078 \)

2. Multiply each isotope's mass by its relative abundance:
   - \( 101.90 \times 0.922 = 93.3538 \)
   - \( 99.90 \times 0.078 = 7.7922 \)

3. Add these values to get the average atomic mass:
   \[
   93.3538 + 7.7922 = 101.146
   \]

### Final Answer
To match the significant figures of the provided data, we should round the result to four significant figures: 

\[
\text{Average Atomic Mass} \approx 101.1 \, \text{amu}
\]

The entry for ruthenium on 98765 ALEKS would be **101.1 amu**.

Would you like more details or have any questions?

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### Follow-up Questions

1. What would the calculation look like if there were more isotopes involved?
2. How do we determine the correct number of significant figures in the final answer?
3. How does the average atomic mass differ on Earth for ruthenium, and why might it vary?
4. Can you explain why isotopic abundances can vary between planets?
5. How does this isotopic information help scientists understand planetary formation?

### Tip
When calculating weighted averages, always convert percentage abundances to decimals before multiplying.

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 | Mass (amu) | Relative Abundance
102 Ru | 101.90 | 92.2%
100 Ru | 99.90 | 7.8%

Use these measurements to complete the entry for ruthenium in the Periodic Table that would be used on 98765 ALEKS. Be sure your answers have the correct number of significant digits.

Calculate the average atomic mass of ruthenium using isotopic data from 98765 ALEKS. Given isotopes with masses 101.90 amu and 99.90 amu and abundances of 92.2% and 7.8%, respectively, this problem illustrates how to determine the weighted atomic mass with correct significant figures.

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