Question:
What is the maximum number of electrons that can be accommodated in a subshell with orbital angular momentum quantum number \(l = 3\)?
What is the maximum number of electrons that can be accommodated in a subshell with orbital angular momentum quantum number \(l = 3\)?
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To quickly find subshell capacities, remember they increase in steps of 4 starting from 2: \(s=2\), \(p=6\), \(d=10\), \(f=14\). This is consistent with the formula \(2(2l+1)\).
Updated On: May 2, 2026
- \(6\)
- \(10\)
- \(14\)
- \(18\)
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The Correct Option is C
Solution and Explanation
Concept:
The maximum number of electrons that can be accommodated in a subshell is given by the formula:
\[
2(2l + 1)
\]
where
\(l\) = azimuthal (orbital angular momentum) quantum number.
This formula accounts for the fact that there are \((2l + 1)\) orbitals in a subshell, and each orbital can hold a maximum of \(2\) electrons (with opposite spins).
Step 1: Substitute the given value of \(l\). Given: \[ l = 3 \] Calculate the number of orbitals: \[ 2l + 1 = 2(3) + 1 = 7 \] Thus, there are \(7\) orbitals in this subshell.
Step 2: Calculate the maximum number of electrons. Since each orbital can accommodate \(2\) electrons: \[ \text{Maximum electrons} = 2 \times 7 = 14 \]
Step 3: Identify the subshell. When \(l = 3\), it corresponds to the f-subshell. The sequence is:
• \(l=0\): s-subshell (2 electrons)
• \(l=1\): p-subshell (6 electrons)
• \(l=2\): d-subshell (10 electrons)
• \(l=3\): f-subshell (14 electrons)
Step 1: Substitute the given value of \(l\). Given: \[ l = 3 \] Calculate the number of orbitals: \[ 2l + 1 = 2(3) + 1 = 7 \] Thus, there are \(7\) orbitals in this subshell.
Step 2: Calculate the maximum number of electrons. Since each orbital can accommodate \(2\) electrons: \[ \text{Maximum electrons} = 2 \times 7 = 14 \]
Step 3: Identify the subshell. When \(l = 3\), it corresponds to the f-subshell. The sequence is:
• \(l=0\): s-subshell (2 electrons)
• \(l=1\): p-subshell (6 electrons)
• \(l=2\): d-subshell (10 electrons)
• \(l=3\): f-subshell (14 electrons)
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