Practice Exercise 2. Three isotopes of silicon occur in nature: 28Si (92.23%), atomic mass 27.97693 amu; 29Si (4.68%), atomic mass 28.97649 amu; and 30Si (3.09%), atomic mass 29.97377 amu. Calculate the atomic weight of silicon.
Answer (2)
Multiply the mass of each isotope by its fractional abundance.
Sum the results to obtain the weighted average atomic mass.
Atomic weight = (0.9223 * 27.97693) + (0.0468 * 28.97649) + (0.0309 * 29.97377) = 28.085411764
The atomic weight of silicon is approximately 28.085411764 amu.
Explanation
Understanding the Problem We are given the percentage abundances and atomic masses of three silicon isotopes and asked to calculate the atomic weight of silicon. The atomic weight is the weighted average of the isotopic masses.
Solution Plan To calculate the atomic weight, we multiply the mass of each isotope by its fractional abundance and sum the results. The fractional abundances are obtained by dividing the percentage abundances by 100.
Calculations The atomic weight of silicon is calculated as follows:
Atomic weight = (fractional abundance of 28Si × mass of 28Si) + (fractional abundance of 29Si × mass of 29Si) + (fractional abundance of 30Si × mass of 30Si)
Atomic weight = (0.9223 × 27.97693 amu) + (0.0468 × 28.97649 amu) + (0.0309 × 29.97377 amu)
Atomic weight = 25.80382 amu + 1.35695 amu + 0.92619 amu
Atomic weight = 28.08696 amu
Final Answer Therefore, the atomic weight of silicon is approximately 28.08696 amu.
Examples
Understanding how to calculate atomic weight is crucial in many fields. For example, in material science, knowing the precise atomic weight of elements helps in designing materials with specific properties. In environmental science, it's used to track the movement and transformation of isotopes in ecosystems. Also, in nuclear chemistry, it is essential for understanding radioactive decay and nuclear reactions. For instance, calculating the atomic weight of a newly discovered element or isotope helps classify it and predict its behavior in chemical reactions.
The atomic weight of silicon is calculated using the isotopic masses and their natural abundances, resulting in an atomic weight of approximately 28.083 amu. This involves converting percentages to fractions, multiplying by the atomic masses, and summing the results. Understanding how to compute atomic weight is essential in various scientific fields.
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