Answer :
To determine the atomic mass of molybdenum on the planetesimal 98765 ALEKS, we need to calculate a weighted average based on the isotopes' masses and their relative abundances. Here's how you can do it step-by-step:
1. Identify the Isotopes and Their Properties:
- Isotope [tex]\(^{98}\text{Mo}\)[/tex]:
- Mass = 97.9 amu
- Relative abundance = 97.5%
- Isotope [tex]\(^{95}\text{Mo}\)[/tex]:
- Mass = 94.9 amu
- Relative abundance = 2.5%
2. Convert Relative Abundances to Fractions:
- For [tex]\(^{98}\text{Mo}\)[/tex], convert 97.5% to a fraction: 97.5% = 0.975
- For [tex]\(^{95}\text{Mo}\)[/tex], convert 2.5% to a fraction: 2.5% = 0.025
3. Calculate the Weighted Average Atomic Mass:
We multiply each isotope's mass by its fractional abundance and add these values together to find the atomic mass.
- Contribution from [tex]\(^{98}\text{Mo}\)[/tex]: [tex]\(97.9 \times 0.975 = 95.5275\)[/tex]
- Contribution from [tex]\(^{95}\text{Mo}\)[/tex]: [tex]\(94.9 \times 0.025 = 2.3725\)[/tex]
Add these contributions together:
[tex]\[
\text{Atomic mass} = 95.5275 + 2.3725 = 97.9
\][/tex]
4. Round the Atomic Mass to 3 Significant Digits:
The calculated atomic mass of molybdenum for the planetesimal 98765 ALEKS, rounded to three significant digits, is 97.8.
This atomic mass is specific to the composition of isotopes on the planetesimal 98765 ALEKS and may differ from the periodic table used on Earth.
1. Identify the Isotopes and Their Properties:
- Isotope [tex]\(^{98}\text{Mo}\)[/tex]:
- Mass = 97.9 amu
- Relative abundance = 97.5%
- Isotope [tex]\(^{95}\text{Mo}\)[/tex]:
- Mass = 94.9 amu
- Relative abundance = 2.5%
2. Convert Relative Abundances to Fractions:
- For [tex]\(^{98}\text{Mo}\)[/tex], convert 97.5% to a fraction: 97.5% = 0.975
- For [tex]\(^{95}\text{Mo}\)[/tex], convert 2.5% to a fraction: 2.5% = 0.025
3. Calculate the Weighted Average Atomic Mass:
We multiply each isotope's mass by its fractional abundance and add these values together to find the atomic mass.
- Contribution from [tex]\(^{98}\text{Mo}\)[/tex]: [tex]\(97.9 \times 0.975 = 95.5275\)[/tex]
- Contribution from [tex]\(^{95}\text{Mo}\)[/tex]: [tex]\(94.9 \times 0.025 = 2.3725\)[/tex]
Add these contributions together:
[tex]\[
\text{Atomic mass} = 95.5275 + 2.3725 = 97.9
\][/tex]
4. Round the Atomic Mass to 3 Significant Digits:
The calculated atomic mass of molybdenum for the planetesimal 98765 ALEKS, rounded to three significant digits, is 97.8.
This atomic mass is specific to the composition of isotopes on the planetesimal 98765 ALEKS and may differ from the periodic table used on Earth.
