Math Problem Statement
Calculate the atomic mass of silicon. The three silicon isotopes have atomic masses and relative abundances of 27.9769 amu (92.2297%), 28.9765 amu (4.6832%) and 29.9738 amu (3.0872%).
Solution
To calculate the atomic mass of silicon, we use the atomic masses and relative abundances of the isotopes. The formula is:
where:
- , , are the atomic masses of the isotopes,
- , , are the fractional abundances of the isotopes (the percentages converted to fractions by dividing by 100).
Given dataTo calculate the atomic mass of silicon, we use the atomic masses and relative abundances of the isotopes. The formula is:
where:
- , , are the atomic masses of the isotopes,
- , , are the fractional abundances of the isotopes (the percentages converted to fractions by dividing by 100).
Given
- amu, ,
- amu, ,
- amu, .
Now, we compute the atomic mass:
Let me calculate that.The atomic mass of silicon, based on the given isotopes and their relative abundances, is approximately 28.0854 amu.
Would you like further details or have any other questions?
Here are 5 related questions to consider:
- How do isotopes affect the chemical behavior of an element?
- Why are certain isotopes more abundant than others in nature?
- What is the significance of using atomic mass in chemical calculations?
- How do mass spectrometers measure atomic masses and relative abundances?
- Can the atomic mass of an element vary slightly depending on the source?
Tip: Atomic mass is a weighted average of the masses of an element’s isotopes, making it slightly different from the mass number of individual isotopes.
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Math Problem Analysis
Mathematical Concepts
Weighted Average
Atomic Mass Calculation
Formulas
Atomic mass = (m1 × f1) + (m2 × f2) + (m3 × f3)
Theorems
-
Suitable Grade Level
Grades 9-12
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