Get detailed and reliable answers to your questions on IDNLearn.com. Ask anything and receive well-informed answers from our community of experienced professionals.
Sagot :
To find the average atomic mass of element [tex]\( M \)[/tex], we first need to consider the atomic masses and relative abundances of its isotopes. The isotopes' data is provided in the table:
| Relative abundance (%) | Atomic mass (amu) |
|------------------------|-------------------|
| 78.99 | 23.9850 |
| 10.00 | 24.9858 |
| 11.01 | 25.9826 |
Here is the step-by-step process:
1. Convert the relative abundances from percentages to fractions:
[tex]\[ \text{Fractional abundance of isotope 1} = \frac{78.99}{100} = 0.7899 \][/tex]
[tex]\[ \text{Fractional abundance of isotope 2} = \frac{10.00}{100} = 0.10 \][/tex]
[tex]\[ \text{Fractional abundance of isotope 3} = \frac{11.01}{100} = 0.1101 \][/tex]
2. Use the formula for average atomic mass:
[tex]\[ \text{Average atomic mass} = (\text{fractional abundance of isotope 1} \times \text{atomic mass of isotope 1}) + (\text{fractional abundance of isotope 2} \times \text{atomic mass of isotope 2}) + (\text{fractional abundance of isotope 3} \times \text{atomic mass of isotope 3}) \][/tex]
3. Substitute the given values into the formula:
[tex]\[ \text{Average atomic mass} = (0.7899 \times 23.9850) + (0.10 \times 24.9858) + (0.1101 \times 25.9826) \][/tex]
4. Compute each term:
[tex]\[ 0.7899 \times 23.9850 = 18.945915 \][/tex]
[tex]\[ 0.10 \times 24.9858 = 2.49858 \][/tex]
[tex]\[ 0.1101 \times 25.9826 = 2.86052026 \][/tex]
5. Sum these values to get the average atomic mass:
[tex]\[ \text{Average atomic mass} = 18.945915 + 2.49858 + 2.86052026 = 24.30501576 \][/tex]
Therefore, the average atomic mass of element [tex]\( M \)[/tex] is approximately [tex]\( 24.30 \)[/tex] amu.
Hence, the correct answer is:
[tex]\[ \boxed{24.30} \][/tex]
| Relative abundance (%) | Atomic mass (amu) |
|------------------------|-------------------|
| 78.99 | 23.9850 |
| 10.00 | 24.9858 |
| 11.01 | 25.9826 |
Here is the step-by-step process:
1. Convert the relative abundances from percentages to fractions:
[tex]\[ \text{Fractional abundance of isotope 1} = \frac{78.99}{100} = 0.7899 \][/tex]
[tex]\[ \text{Fractional abundance of isotope 2} = \frac{10.00}{100} = 0.10 \][/tex]
[tex]\[ \text{Fractional abundance of isotope 3} = \frac{11.01}{100} = 0.1101 \][/tex]
2. Use the formula for average atomic mass:
[tex]\[ \text{Average atomic mass} = (\text{fractional abundance of isotope 1} \times \text{atomic mass of isotope 1}) + (\text{fractional abundance of isotope 2} \times \text{atomic mass of isotope 2}) + (\text{fractional abundance of isotope 3} \times \text{atomic mass of isotope 3}) \][/tex]
3. Substitute the given values into the formula:
[tex]\[ \text{Average atomic mass} = (0.7899 \times 23.9850) + (0.10 \times 24.9858) + (0.1101 \times 25.9826) \][/tex]
4. Compute each term:
[tex]\[ 0.7899 \times 23.9850 = 18.945915 \][/tex]
[tex]\[ 0.10 \times 24.9858 = 2.49858 \][/tex]
[tex]\[ 0.1101 \times 25.9826 = 2.86052026 \][/tex]
5. Sum these values to get the average atomic mass:
[tex]\[ \text{Average atomic mass} = 18.945915 + 2.49858 + 2.86052026 = 24.30501576 \][/tex]
Therefore, the average atomic mass of element [tex]\( M \)[/tex] is approximately [tex]\( 24.30 \)[/tex] amu.
Hence, the correct answer is:
[tex]\[ \boxed{24.30} \][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.