Question:
How many electrons in an atom have the following quantum numbers? \(N = 3, l = 0\)
How many electrons in an atom have the following quantum numbers? \(N = 3, l = 0\)
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l = 0 means the s subshell, and an s subshell has only one orbital.
Updated On: Jul 2, 2026
- 4
- 2
- 6
- 8
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The Correct Option is B
Solution and Explanation
Step 1: The principal quantum number \(n = 3\) tells us we are looking at the third shell. The azimuthal quantum number \(l = 0\) tells us we are looking only at the s subshell of that shell, which is the 3s subshell.
Step 2: For a given value of \(l\), the number of orbitals is \(2l + 1\). For \(l = 0\): \[2(0) + 1 = 1\] So the 3s subshell has just 1 orbital.
Step 3: By the Pauli exclusion principle, each orbital can hold a maximum of 2 electrons, with opposite spins. So the maximum number of electrons with \(n = 3, l = 0\) is \[1 \times 2 = 2\]
\[\boxed{2 \text{ electrons}}\]
Step 2: For a given value of \(l\), the number of orbitals is \(2l + 1\). For \(l = 0\): \[2(0) + 1 = 1\] So the 3s subshell has just 1 orbital.
Step 3: By the Pauli exclusion principle, each orbital can hold a maximum of 2 electrons, with opposite spins. So the maximum number of electrons with \(n = 3, l = 0\) is \[1 \times 2 = 2\]
\[\boxed{2 \text{ electrons}}\]
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