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%).

To calculate the atomic mass of silicon, we use the atomic masses and relative abundances of the isotopes. The formula is:

\[
\text{Atomic mass} = (m_1 \times f_1) + (m_2 \times f_2) + (m_3 \times f_3)
\]

where:
- \(m_1\), \(m_2\), \(m_3\) are the atomic masses of the isotopes,
- \(f_1\), \(f_2\), \(f_3\) 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:

\[
\text{Atomic mass} = (m_1 \times f_1) + (m_2 \times f_2) + (m_3 \times f_3)
\]

where:
- \(m_1\), \(m_2\), \(m_3\) are the atomic masses of the isotopes,
- \(f_1\), \(f_2\), \(f_3\) are the fractional abundances of the isotopes (the percentages converted to fractions by dividing by 100).

Given 
- \(m_1 = 27.9769\) amu, \(f_1 = 92.2297\% = 0.922297\),
- \(m_2 = 28.9765\) amu, \(f_2 = 4.6832\% = 0.046832\),
- \(m_3 = 29.9738\) amu, \(f_3 = 3.0872\% = 0.030872\).

Now, we compute the atomic mass:

\[
\text{Atomic mass} = (27.9769 \times 0.922297) + (28.9765 \times 0.046832) + (29.9738 \times 0.030872)
\]

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:
1. How do isotopes affect the chemical behavior of an element?
2. Why are certain isotopes more abundant than others in nature?
3. What is the significance of using atomic mass in chemical calculations?
4. How do mass spectrometers measure atomic masses and relative abundances?
5. 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.

Learn how to calculate the atomic mass of silicon using the weighted average of its three isotopes: 27.9769 amu (92.2297%), 28.9765 amu (4.6832%), and 29.9738 amu (3.0872%). This problem covers key concepts in atomic mass calculation and is suitable for Grades 9-12.

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