Question:medium

Which of the following set of quantum numbers represent the electron with highest energy?

Show Hint

$(n+l)$ rule: Higher sum = higher energy!
Updated On: Jun 6, 2026
  • $n=3, l=0, m=0, s=+1/2$
  • $n=3, l=1, m=1, s=-1/2$
  • $n=3, l=2, m=1, s=+1/2$
  • $n=4, l=0, m=0, s=-1/2$
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: What decides the energy of an electron.
In a multi-electron atom the energy of an orbital is fixed by the $(n+l)$ rule, also called the Aufbau rule. A bigger $(n+l)$ value means a higher energy orbital.

Step 2: The tie-breaker rule.
If two orbitals have the same $(n+l)$ value, then the one with the larger $n$ has higher energy. So we just compute $(n+l)$ for each choice.

Step 3: Work out each option.
Option 1: $n=3, l=0 \Rightarrow n+l = 3$ (this is $3s$).
Option 2: $n=3, l=1 \Rightarrow n+l = 4$ (this is $3p$).
Option 3: $n=3, l=2 \Rightarrow n+l = 5$ (this is $3d$).
Option 4: $n=4, l=0 \Rightarrow n+l = 4$ (this is $4s$).

Step 4: Pick the largest.
The values are $3, 4, 5, 4$. The biggest is $5$, which belongs to Option 3, the $3d$ electron.

Step 5: Conclusion.
So the electron with the highest energy is the one with $n=3, l=2, m=1, s=+1/2$. \[ \boxed{n=3,\ l=2\ (3d)} \]
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