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Answer :
Sure! To determine the atomic weight of molybdenum on the planetesimal 98765 ALEKS, we will use the data provided about its isotopes. Here's how you can calculate it step by step:
1. Understand the Data:
- We are given two isotopes of molybdenum, each with its atomic mass in atomic mass units (amu) and a relative abundance in percentage.
- The two isotopes are:
- [tex]\({}^{100}\text{Mo}\)[/tex] with a mass of 99.9 amu and an abundance of 90.6%.
- [tex]\({}^{96}\text{Mo}\)[/tex] with a mass of 95.9 amu and an abundance of 9.4%.
2. Convert Abundance Percentages into Fractions:
- To work with these percentages mathematically, we convert them into fractions by dividing by 100:
- For [tex]\({}^{100}\text{Mo}\)[/tex]: [tex]\(\frac{90.6}{100} = 0.906\)[/tex]
- For [tex]\({}^{96}\text{Mo}\)[/tex]: [tex]\(\frac{9.4}{100} = 0.094\)[/tex]
3. Calculate the Weighted Average (Atomic Weight):
- The atomic weight is calculated by multiplying the mass of each isotope by its respective fractional abundance, and then adding these values together:
[tex]\[
\text{Atomic weight of molybdenum} = (99.9 \, \text{amu} \times 0.906) + (95.9 \, \text{amu} \times 0.094)
\][/tex]
4. Calculate Each Contribution:
- Contribution of [tex]\({}^{100}\text{Mo}\)[/tex]: [tex]\(99.9 \, \text{amu} \times 0.906 = 90.5994\)[/tex]
- Contribution of [tex]\({}^{96}\text{Mo}\)[/tex]: [tex]\(95.9 \, \text{amu} \times 0.094 = 9.0226\)[/tex]
5. Add the Contributions:
[tex]\[
90.5994 + 9.0226 = 99.622
\][/tex]
6. Determine the Final Result with Significant Figures:
- Since the given data generally has four significant figures (e.g., 99.9), we should round the result to four significant figures:
- The atomic weight of molybdenum for 98765 ALEKS is approximately [tex]\(99.62\)[/tex].
Therefore, if you were to complete the entry for molybdenum on the periodic table for planetesimal 98765 ALEKS, the atomic weight would be recorded as approximately 99.62.
1. Understand the Data:
- We are given two isotopes of molybdenum, each with its atomic mass in atomic mass units (amu) and a relative abundance in percentage.
- The two isotopes are:
- [tex]\({}^{100}\text{Mo}\)[/tex] with a mass of 99.9 amu and an abundance of 90.6%.
- [tex]\({}^{96}\text{Mo}\)[/tex] with a mass of 95.9 amu and an abundance of 9.4%.
2. Convert Abundance Percentages into Fractions:
- To work with these percentages mathematically, we convert them into fractions by dividing by 100:
- For [tex]\({}^{100}\text{Mo}\)[/tex]: [tex]\(\frac{90.6}{100} = 0.906\)[/tex]
- For [tex]\({}^{96}\text{Mo}\)[/tex]: [tex]\(\frac{9.4}{100} = 0.094\)[/tex]
3. Calculate the Weighted Average (Atomic Weight):
- The atomic weight is calculated by multiplying the mass of each isotope by its respective fractional abundance, and then adding these values together:
[tex]\[
\text{Atomic weight of molybdenum} = (99.9 \, \text{amu} \times 0.906) + (95.9 \, \text{amu} \times 0.094)
\][/tex]
4. Calculate Each Contribution:
- Contribution of [tex]\({}^{100}\text{Mo}\)[/tex]: [tex]\(99.9 \, \text{amu} \times 0.906 = 90.5994\)[/tex]
- Contribution of [tex]\({}^{96}\text{Mo}\)[/tex]: [tex]\(95.9 \, \text{amu} \times 0.094 = 9.0226\)[/tex]
5. Add the Contributions:
[tex]\[
90.5994 + 9.0226 = 99.622
\][/tex]
6. Determine the Final Result with Significant Figures:
- Since the given data generally has four significant figures (e.g., 99.9), we should round the result to four significant figures:
- The atomic weight of molybdenum for 98765 ALEKS is approximately [tex]\(99.62\)[/tex].
Therefore, if you were to complete the entry for molybdenum on the periodic table for planetesimal 98765 ALEKS, the atomic weight would be recorded as approximately 99.62.
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