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Structure of Atom question

2022 · 24 Jun · Shift 1 · Q2
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Structure of Atom question

2022 · 24 Jun · Shift 1 · Q2

JEE MainChemistryStructure of AtomMCQ+4 / −1
Consider the following pairs of electrons (A) (a) n = 3, lll= 1, m1 = 1, ms = +12{1 \over 2}21​(b) n = 3, 1 = 2, m1 = 1, ms = +12{1 \over 2}21​(B) (a) n = 3, lll= 2, m1 =−-− 2, ms = −12-{1 \over 2}−21​(b) n = 3, lll= 2, m1 =−-− 1, ms = −12-{1 \over 2}−21​(C) (a) n = 4, lll= 2, m1 = 2, ms = +12{1 \over 2}21​(b) n = 3, lll= 2, m1 = 2, ms = +12{1 \over 2}21​ The pairs of electrons present in degenerate orbitals is/are :
  1. A
    Only (A)
  2. B
    Only (B)
  3. C
    Only (C)
  4. D
    (B) and (C)
View written solutionFree

Correct answer: B

  1. Condition for degenerate orbitals

    Electrons are in degenerate orbitals if they have the same energy.

    For multi-electron atoms, the energy of an orbital depends mainly on nnn and lll.
    So, orbitals are degenerate when they have the same nnn and same lll; different mlm_lml​ values within the same subshell are degenerate.

    Also, msm_sms​ does not affect orbital energy in the absence of an external magnetic field.

  2. Check pair (A)

    • Electron (a): n=3, l=1, ml=1, ms=+12n=3,\ l=1,\ m_l=1,\ m_s=+\frac{1}{2}n=3, l=1, ml​=1, ms​=+21​
      This is a 3p3p3p orbital.
    • Electron (b): n=3, l=2, ml=1, ms=+12n=3,\ l=2,\ m_l=1,\ m_s=+\frac{1}{2}n=3, l=2, ml​=1, ms​=+21​
      This is a 3d3d3d orbital.

    Since lll is different (1≠21 \neq 21=2), they belong to different subshells, so they are not degenerate.

  3. Check pair (B)

    • Electron (a): n=3, l=2, ml=−2, ms=−12n=3,\ l=2,\ m_l=-2,\ m_s=-\frac{1}{2}n=3, l=2, ml​=−2, ms​=−21​
    • Electron (b): n=3, l=2, ml=−1, ms=−12n=3,\ l=2,\ m_l=-1,\ m_s=-\frac{1}{2}n=3, l=2, ml​=−1, ms​=−21​

    Here both have the same n=3n=3n=3 and l=2l=2l=2, so both are in the 3d3d3d subshell.
    Different mlm_lml​ values correspond to different orbitals within the same subshell, which are degenerate.

    Hence, (B) is correct.

  4. Check pair (C)

    • Electron (a): n=4, l=2, ml=2, ms=+12n=4,\ l=2,\ m_l=2,\ m_s=+\frac{1}{2}n=4, l=2, ml​=2, ms​=+21​
      This is a 4d4d4d orbital.
    • Electron (b): n=3, l=2, ml=2, ms=+12n=3,\ l=2,\ m_l=2,\ m_s=+\frac{1}{2}n=3, l=2, ml​=2, ms​=+21​
      This is a 3d3d3d orbital.

    Since nnn is different (4≠34 \neq 34=3), these are different subshells with different energies, so they are not degenerate.

  5. Final conclusion

    Only pair (B) consists of electrons in degenerate orbitals.

    Therefore, the correct option is:

    B: Only (B)\boxed{\text{B: Only (B)}}B: Only (B)​

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