KCET · Chemistry · Structure of Atom

The two electrons have the following set of quantum numbers :
\[
\begin{array}{l}
P=3,2,-2,+\frac{1}{2} \\
Q=3,0,0,+\frac{1}{2}
\end{array}
\]
Which of the following statement is true?

A \( P \) and \( Q \) have same energy
B \( P \) has greater energy than \( Q \)
C \( P \) has lesser energy than \( Q \)
D \( \mathrm{P} \) and \( \mathrm{Q} \) represent same electron

Verified Solution

Answer & Solution

Correct Answer

(B) \( P \) has greater energy than \( Q \)

Step-by-step Solution

Detailed explanation

For electron \(P\), the values of quantum numbers are \(n=3, I=2, m l=-2\) and \(s=+1 / 2\). For electron \(Q\) quantum numbers are \(n=3, I=0, m l=0\) and \(s=+1 / 2\). Therefore, from the quantum number values, electron \(P\) belongs to \(3 d-\) orbital and electron \(Q\) to \(3 s\) - orbital. Energy of the orbital is \(s < p < d < f\).
Hence, energy of electron \(P\) is higher than electron \(Q\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The two electrons have the following set of quantum numbers :\[\begin{array}{l}P=3,2,-2,+\frac{1}{2} \\Q=3,0,0,+\frac{1}{2}\end{array}\]Which of the following statement is true?

Step-by-step Solution

The two electrons have the following set of quantum numbers :
\[
\begin{array}{l}
P=3,2,-2,+\frac{1}{2} \\
Q=3,0,0,+\frac{1}{2}
\end{array}
\]
Which of the following statement is true?