JEE Main · 2019 · Shift-IhardATOM-126

Quantum numbers of four electrons are given below: I. n=4,l=2, ml=-2, ms=-12 II. n=3,l=2, ml=1, ms=+12 III. n=4,l=1,…

Structure of Atom · Class 11 · JEE Main Previous Year Question

Question

Quantum numbers of four electrons are given below:

I. n=4,l=2,ml=−2,ms=−12n=4,l=2, m_l=-2, m_s=-\frac{1}{2} II. n=3,l=2,ml=1,ms=+12n=3,l=2, m_l=1, m_s=+\frac{1}{2} III. n=4,l=1,ml=0,ms=+12n=4,l=1, m_l=0, m_s=+\frac{1}{2} IV. n=3,l=1,ml=1ms=−12n=3,l=1, m_l=1 m_s=-\frac{1}{2}

Correct order of increasing energies:

Options
  1. a

    I < III < II < IV

  2. b

    IV < II < III < I

    ✓
  3. c

    I < II < III < II

  4. d

    IV < III < II < I

Correct Answerb

IV < II < III < I

Detailed Solution

🧠 The n+ln+l Hierarchy To rank orbital energies, calculate the n+ln+l sum for each. Lower sum = Lower energy. For ties, lower nn = Lower energy.

🗺️ The Energy Audit

  • IV: n=3,l=1→4n=3, l=1 \to 4 (3p)
  • II: n=3,l=2→5n=3, l=2 \to 5 (3d)
  • III: n=4,l=1→5n=4, l=1 \to 5 (4p)
  • I: n=4,l=2→6n=4, l=2 \to 6 (4d)

Ranking:

  1. IV (4) is lowest.
  2. II vs III: Both are 5. II (n=3n=3) is lower than III (n=4n=4).
  3. I (6) is highest. Order: IV < II < III < I.

⚡ The "Shell Tie-Breaker" When n+ln+l is identical (like 3d3d and 4p4p), the electron in the inner shell (n=3n=3) feels a stronger nuclear pull despite the ll-shielding, putting it slightly lower in the potential well.

⚠️ Common Traps Mixing up the ll values: p=1,d=2p=1, d=2. If you mistake dd for 1, your entire ranking will flip!

Answer: (b)\boxed{\text{Answer: (b)}}

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