Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine the average atomic mass of an element with isotopes [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex], one must use the concept of the weighted average. This involves multiplying the mass of each isotope by its relative abundance (expressed as a percentage) and then summing these values. Each percentage must be converted from a percent to a fraction (by dividing by 100) before performing the multiplication.
Given the choices:
Choice A:
[tex]\[ \frac{\text{(mass of } A + \text{ mass of } B + \text{ mass of } C)}{3} \][/tex]
This simply averages the masses of the isotopes without considering their relative abundances. Hence, it is not correct.
Choice B:
[tex]\[ \frac{[(\text{ mass of } A) \times (\% \text{ of } A) + (\text{ mass of } B) \times (\% \text{ of } B) + (\text{ mass of } C) \times (\% \text{ of } C)]}{3} \][/tex]
This formula incorrectly divides the sum of the weighted masses by 3, which is not how weighted averages are calculated.
Choice C:
[tex]\[ \frac{\text{(mass of } A)}{(\% \text{ of } A)} + \frac{\text{(mass of B)}}{(\% \text{ of } B)} + \frac{\text{(mass of } C)}{(\% \text{ of } C)} \][/tex]
This formula reverses the intended operation by dividing the mass of each isotope by their respective percentages. This does not produce a correct weighted average.
Choice D:
[tex]\[ (\text{mass of } A) \times (\% \text{ of } A) + (\text{mass of } B) \times (\% \text{ of } B) + (\text{mass of } C) \times (\% \text{ of } C) \][/tex]
This choice calculates the average atomic mass correctly by taking the weighted sum of the masses of the isotopes multiplied by their relative abundances.
Therefore, the correct choice is:
[tex]\[ \boxed{D} \][/tex]
Given the choices:
Choice A:
[tex]\[ \frac{\text{(mass of } A + \text{ mass of } B + \text{ mass of } C)}{3} \][/tex]
This simply averages the masses of the isotopes without considering their relative abundances. Hence, it is not correct.
Choice B:
[tex]\[ \frac{[(\text{ mass of } A) \times (\% \text{ of } A) + (\text{ mass of } B) \times (\% \text{ of } B) + (\text{ mass of } C) \times (\% \text{ of } C)]}{3} \][/tex]
This formula incorrectly divides the sum of the weighted masses by 3, which is not how weighted averages are calculated.
Choice C:
[tex]\[ \frac{\text{(mass of } A)}{(\% \text{ of } A)} + \frac{\text{(mass of B)}}{(\% \text{ of } B)} + \frac{\text{(mass of } C)}{(\% \text{ of } C)} \][/tex]
This formula reverses the intended operation by dividing the mass of each isotope by their respective percentages. This does not produce a correct weighted average.
Choice D:
[tex]\[ (\text{mass of } A) \times (\% \text{ of } A) + (\text{mass of } B) \times (\% \text{ of } B) + (\text{mass of } C) \times (\% \text{ of } C) \][/tex]
This choice calculates the average atomic mass correctly by taking the weighted sum of the masses of the isotopes multiplied by their relative abundances.
Therefore, the correct choice is:
[tex]\[ \boxed{D} \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.