Question:
Maximum number of electrons possible with spin quantum number
\[
+\frac{1}{2}
\]
with principal quantum number \(n=4\) in an atom is:
Maximum number of electrons possible with spin quantum number
\[
+\frac{1}{2}
\]
with principal quantum number \(n=4\) in an atom is:
Show Hint
Maximum electrons in the \(n^{th}\) shell:
\[
2n^2
\]
and electrons with a particular spin orientation are half of this value.
Updated On: Jun 24, 2026
- \(16\)
- \(9\)
- \(4\)
- \(25\)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Recall the maximum number of electrons in a shell.
For a shell having principal quantum number \[ n, \] maximum number of electrons is \[ 2n^2 \] For \[ n=4, \] maximum electrons are \[ 2(4)^2=32 \]
Step 2: Understand spin orientation.
Each orbital can accommodate two electrons having opposite spins: \[ +\frac{1}{2} \quad \text{and} \quad -\frac{1}{2} \] Thus, half the electrons can have spin \[ +\frac{1}{2} \]
Step 3: Calculate the required number.
\[ \frac{32}{2}=16 \]
Step 4: Final conclusion.
Hence, the maximum number of electrons having spin quantum number \[ +\frac{1}{2} \] is \[ \boxed{16} \]
For a shell having principal quantum number \[ n, \] maximum number of electrons is \[ 2n^2 \] For \[ n=4, \] maximum electrons are \[ 2(4)^2=32 \]
Step 2: Understand spin orientation.
Each orbital can accommodate two electrons having opposite spins: \[ +\frac{1}{2} \quad \text{and} \quad -\frac{1}{2} \] Thus, half the electrons can have spin \[ +\frac{1}{2} \]
Step 3: Calculate the required number.
\[ \frac{32}{2}=16 \]
Step 4: Final conclusion.
Hence, the maximum number of electrons having spin quantum number \[ +\frac{1}{2} \] is \[ \boxed{16} \]
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