The table below gives the atomic mass and relative abundance values for the three isotopes of element M.
| Relative abundance (%) | Atomic mass (amu) |
| :---------------------- | :----------------- |
| 78.99 | 23.9850 |
| 10.00 | 24.9858 |
| 11.01 | 25.9826 |
What is the average atomic mass (in amu) of element M?
Answer (1)
Convert the relative abundances from percentages to decimals.
Multiply each isotope's decimal abundance by its atomic mass.
Sum the results to obtain the average atomic mass.
The average atomic mass of element M is approximately 24.30 amu.
Explanation
Understanding the Problem We are given the relative abundances and atomic masses of three isotopes of element M. Our goal is to calculate the average atomic mass of element M. The average atomic mass is the weighted average of the atomic masses of the isotopes, where the weights are the relative abundances.
Converting Percentages to Decimals First, we need to convert the relative abundances from percentages to decimals. This is done by dividing each percentage by 100:
Relative abundance of isotope 1: 78.99% = 100 78.99 = 0.7899
Relative abundance of isotope 2: 10.00% = 100 10.00 = 0.1000
Relative abundance of isotope 3: 11.01% = 100 11.01 = 0.1101
Calculating Weighted Masses Next, we multiply each isotope's decimal abundance by its atomic mass:
Isotope 1: 0.7899 × 23.9850 = 18.9451015
Isotope 2: 0.1000 × 24.9858 = 2.49858
Isotope 3: 0.1101 × 25.9826 = 2.86068426
Summing Weighted Masses Finally, we sum the results from the previous step to obtain the average atomic mass:
Average atomic mass = 18.9451015 + 2.49858 + 2.86068426 = 24.30436576
Final Answer Therefore, the average atomic mass of element M is approximately 24.30 amu.
Examples
The concept of average atomic mass is crucial in various fields. For instance, in chemistry, it helps in determining the molar mass of a compound, which is essential for stoichiometric calculations in chemical reactions. In material science, understanding the isotopic composition and average atomic mass is vital for predicting the properties of materials. For example, enriched uranium used in nuclear reactors relies on precise knowledge of isotopic masses and abundances to control nuclear reactions effectively.
