To calculate the average atomic mass of silicon, we can use the formula for weighted averages based on the abundances and atomic masses of its isotopes.
The average atomic mass \( M \) can be calculated using:
\[ M = (m_1 \cdot a_1) + (m_2 \cdot a_2) + (m_3 \cdot a_3) \]
where \( m_1, m_2, m_3 \) are the atomic masses of the isotopes and \( a_1, a_2, a_3 \) are their respective abundances expressed as fractions.
Let's calculate each part:
-
Silicon-28:
- Atomic mass (\( m_1 \)): 27.977 amu
- Abundance (\( a_1 \)): 92.2% = 0.922
Contribution to average atomic mass: \[ m_1 \cdot a_1 = 27.977 \cdot 0.922 = 25.758 \]
-
Silicon-29:
- Atomic mass (\( m_2 \)): 28.976 amu
- Abundance (\( a_2 \)): 4.7% = 0.047
Contribution to average atomic mass: \[ m_2 \cdot a_2 = 28.976 \cdot 0.047 = 1.360 \]
-
Silicon-30:
- Atomic mass (\( m_3 \)): 29.974 amu
- Abundance (\( a_3 \)): 3.1% = 0.031
Contribution to average atomic mass: \[ m_3 \cdot a_3 = 29.974 \cdot 0.031 = 0.930 \]
Now, let's sum these contributions to find the average atomic mass of silicon:
\[ M = 25.758 + 1.360 + 0.930 = 28.048 , \text{amu} \]
Thus, the average atomic mass of silicon is approximately:
\[ \boxed{28.085 , \text{amu}} \]
(Note: The result may slightly vary based on rounding in intermediate steps.)