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Answer :
Sure! Let's solve the problem step by step.
First, we need to find the weighted average mass of the isotopes of the imaginary element Xq. This weighted average is called the atomic weight. The atomic weight takes into account both the mass of each isotope and its abundance in the sample.
We are provided with the following information:
- The mass of the [tex]\(^{100}Xq\)[/tex] isotope is 100.0 amu.
- The mass of the [tex]\(^{102}Xq\)[/tex] isotope is 102.0 amu.
- The abundance of the [tex]\(^{100}Xq\)[/tex] isotope is 20.0%.
- The abundance of the [tex]\(^{102}Xq\)[/tex] isotope is 80.0%.
To find the atomic weight, we will:
1. Convert the abundances from percentages to fractions.
- For [tex]\(^{100}Xq\)[/tex]: [tex]\(20.0\%\)[/tex] is equivalent to 0.20.
- For [tex]\(^{102}Xq\)[/tex]: [tex]\(80.0\%\)[/tex] is equivalent to 0.80.
2. Multiply the mass of each isotope by its fractional abundance:
- Contribution of [tex]\(^{100}Xq\)[/tex]: [tex]\(100.0 \text{ amu} \times 0.20 = 20.0 \text{ amu}\)[/tex]
- Contribution of [tex]\(^{102}Xq\)[/tex]: [tex]\(102.0 \text{ amu} \times 0.80 = 81.6 \text{ amu}\)[/tex]
3. Add these contributions together to get the atomic weight:
- Atomic weight of Xq = [tex]\(20.0 \text{ amu} + 81.6 \text{ amu} = 101.6 \text{ amu}\)[/tex]
Therefore, the atomic weight of element Xq is 101.6 amu.
Given the provided options:
- 100.4 amu
- 1010.5 amu
- 202.0 amu
- 101.0 amu
- 100.2 amu
The correct answer is not explicitly listed among the options, but the closest available answer is:
101.0 amu
This seems to be a case of slight difference due to rounding. Based on the calculation, this is the closest numerical option.
First, we need to find the weighted average mass of the isotopes of the imaginary element Xq. This weighted average is called the atomic weight. The atomic weight takes into account both the mass of each isotope and its abundance in the sample.
We are provided with the following information:
- The mass of the [tex]\(^{100}Xq\)[/tex] isotope is 100.0 amu.
- The mass of the [tex]\(^{102}Xq\)[/tex] isotope is 102.0 amu.
- The abundance of the [tex]\(^{100}Xq\)[/tex] isotope is 20.0%.
- The abundance of the [tex]\(^{102}Xq\)[/tex] isotope is 80.0%.
To find the atomic weight, we will:
1. Convert the abundances from percentages to fractions.
- For [tex]\(^{100}Xq\)[/tex]: [tex]\(20.0\%\)[/tex] is equivalent to 0.20.
- For [tex]\(^{102}Xq\)[/tex]: [tex]\(80.0\%\)[/tex] is equivalent to 0.80.
2. Multiply the mass of each isotope by its fractional abundance:
- Contribution of [tex]\(^{100}Xq\)[/tex]: [tex]\(100.0 \text{ amu} \times 0.20 = 20.0 \text{ amu}\)[/tex]
- Contribution of [tex]\(^{102}Xq\)[/tex]: [tex]\(102.0 \text{ amu} \times 0.80 = 81.6 \text{ amu}\)[/tex]
3. Add these contributions together to get the atomic weight:
- Atomic weight of Xq = [tex]\(20.0 \text{ amu} + 81.6 \text{ amu} = 101.6 \text{ amu}\)[/tex]
Therefore, the atomic weight of element Xq is 101.6 amu.
Given the provided options:
- 100.4 amu
- 1010.5 amu
- 202.0 amu
- 101.0 amu
- 100.2 amu
The correct answer is not explicitly listed among the options, but the closest available answer is:
101.0 amu
This seems to be a case of slight difference due to rounding. Based on the calculation, this is the closest numerical option.
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