Type the correct answer in the box. Round your answer to the nearest hundredth.
Element $X$ has two isotopes. The table gives information about these isotopes.
| Isotope | Atomic Mass (amu) | Abundance (%) |
|---|---|---|
| $X-63$ | 62.9296 | 69.15 |
| $X-65$ | 64.9278 | 30.85 |
The average atomic mass of element $X$ is $\square$ amu.
Answer (2)
Multiply the atomic mass of each isotope by its fractional abundance.
Sum the results to obtain the weighted average.
Round the result to the nearest hundredth.
The average atomic mass of element X is 63.53 amu.
Explanation
Understanding the Problem We are given the atomic masses and abundances of two isotopes of element X, namely X-63 and X-65. We need to calculate the average atomic mass of element X. The average atomic mass is the weighted average of the atomic masses of the isotopes, where the weights are the abundances.
Solution Plan To calculate the average atomic mass, we multiply the atomic mass of each isotope by its fractional abundance and then sum the results. The fractional abundance is the percentage abundance divided by 100.
Calculations The atomic mass of X-63 is 62.9296 amu and its abundance is 69.15%, which as a decimal is 0.6915. The atomic mass of X-65 is 64.9278 amu and its abundance is 30.85%, which as a decimal is 0.3085. Therefore, the average atomic mass is calculated as follows:
( 62.9296 × 0.6915 ) + ( 64.9278 × 0.3085 )
Calculating each term:
62.9296 × 0.6915 = 43.5125034
64.9278 × 0.3085 = 20.0201753
Adding these together:
43.5125034 + 20.0201753 = 63.5326787
Rounding this to the nearest hundredth gives 63.53.
Final Answer The average atomic mass of element X is approximately 63.53 amu.
Examples
Understanding average atomic mass is crucial in various fields. For instance, in chemistry, it helps in calculating the molar mass of compounds containing the element, which is essential for stoichiometric calculations in chemical reactions. In material science, knowing the isotopic composition and average atomic mass can influence the properties of materials, such as their density and nuclear characteristics. For example, enriched uranium used in nuclear reactors relies on precise knowledge of uranium isotopes and their average atomic mass to control the nuclear chain reaction.
To find the average atomic mass of element X, we calculate a weighted average based on the atomic masses and abundances of its isotopes. After performing the calculations, the average atomic mass is found to be approximately 63.55 amu. This value helps in understanding the isotopic composition of element X.
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