Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To find the average atomic mass of element [tex]$X$[/tex] given the two isotopes, we need to perform a weighted average calculation. Here are the steps:
1. Identify the masses and their corresponding abundances:
- Isotope X-63 has a mass of 62.9296 amu and an abundance of 69.15%.
- Isotope X-65 has a mass of 64.9278 amu and an abundance of 30.85%.
2. Convert abundance percentages to fractions:
- Abundance of X-63 as a fraction: [tex]\( \frac{69.15}{100} = 0.6915 \)[/tex]
- Abundance of X-65 as a fraction: [tex]\( \frac{30.85}{100} = 0.3085 \)[/tex]
3. Calculate the weighted average:
We multiply each mass by its corresponding fraction and then add the results:
[tex]\[ \text{Average Atomic Mass} = (62.9296 \times 0.6915) + (64.9278 \times 0.3085) \][/tex]
4. Perform the multiplication and addition:
- For X-63: [tex]\( 62.9296 \times 0.6915 = 43.5112 \)[/tex]
- For X-65: [tex]\( 64.9278 \times 0.3085 = 20.0348 \)[/tex]
- Add these values: [tex]\( 43.5112 + 20.0348 = 63.546 \)[/tex]
5. Round the result to the nearest hundredth:
- The average atomic mass rounded to the nearest hundredth is [tex]\( 63.55 \)[/tex].
Therefore, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 63.55 \)[/tex] amu.
1. Identify the masses and their corresponding abundances:
- Isotope X-63 has a mass of 62.9296 amu and an abundance of 69.15%.
- Isotope X-65 has a mass of 64.9278 amu and an abundance of 30.85%.
2. Convert abundance percentages to fractions:
- Abundance of X-63 as a fraction: [tex]\( \frac{69.15}{100} = 0.6915 \)[/tex]
- Abundance of X-65 as a fraction: [tex]\( \frac{30.85}{100} = 0.3085 \)[/tex]
3. Calculate the weighted average:
We multiply each mass by its corresponding fraction and then add the results:
[tex]\[ \text{Average Atomic Mass} = (62.9296 \times 0.6915) + (64.9278 \times 0.3085) \][/tex]
4. Perform the multiplication and addition:
- For X-63: [tex]\( 62.9296 \times 0.6915 = 43.5112 \)[/tex]
- For X-65: [tex]\( 64.9278 \times 0.3085 = 20.0348 \)[/tex]
- Add these values: [tex]\( 43.5112 + 20.0348 = 63.546 \)[/tex]
5. Round the result to the nearest hundredth:
- The average atomic mass rounded to the nearest hundredth is [tex]\( 63.55 \)[/tex].
Therefore, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 63.55 \)[/tex] amu.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.