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Structure of Atom question

2023 · 31 Jan · Shift 2 · Q7
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Structure of Atom question

2023 · 31 Jan · Shift 2 · Q7

JEE MainChemistryStructure of AtomMCQ+4 / −1
Arrange the following orbitals in decreasing order of energy. A. n=3,l=0, m=0\mathrm{n}=3, \mathrm{l}=0, \mathrm{~m}=0n=3,l=0, m=0 B. n=4,l=0, m=0\mathrm{n}=4, \mathrm{l}=0, \mathrm{~m}=0n=4,l=0, m=0 C. n=3,l=1, m=0\mathrm{n}=3, \mathrm{l}=1, \mathrm{~m}=0n=3,l=1, m=0 D. n=3,l=2, m=1\mathrm{n}=3, \mathrm{l}=2, \mathrm{~m}=1n=3,l=2, m=1 The correct option for the order is :
  1. A
    B>D>C>A\mathrm{B}\gt \mathrm{D}\gt \mathrm{C}\gt \mathrm{A}B>D>C>A
  2. B
    A>C>B>D\mathrm{A}\gt \mathrm{C}\gt \mathrm{B}\gt \mathrm{D}A>C>B>D
  3. C
    D>B>A>C\mathrm{D}\gt \mathrm{B}\gt \mathrm{A}\gt \mathrm{C}D>B>A>C
  4. D
    D>B>C>A\mathrm{D}\gt \mathrm{B}\gt \mathrm{C}\gt \mathrm{A}D>B>C>A
View written solutionFree

Correct answer: D

  1. Identify the orbitals

Given quantum numbers:

  • A: n=3, l=0⇒3sn=3,\ l=0 \Rightarrow 3sn=3, l=0⇒3s
  • B: n=4, l=0⇒4sn=4,\ l=0 \Rightarrow 4sn=4, l=0⇒4s
  • C: n=3, l=1⇒3pn=3,\ l=1 \Rightarrow 3pn=3, l=1⇒3p
  • D: n=3, l=2⇒3dn=3,\ l=2 \Rightarrow 3dn=3, l=2⇒3d

The magnetic quantum number mmm does not affect energy for these orbitals in the usual ordering.

  1. Use the (n+l)(n+l)(n+l) rule

For multi-electron atoms, orbital energy increases with increasing value of (n+l)(n+l)(n+l). If two orbitals have the same (n+l)(n+l)(n+l) value, then the orbital with higher nnn has higher energy.

Now calculate:

  • For 3s3s3s: n+l=3+0=3n+l=3+0=3n+l=3+0=3
  • For 4s4s4s: n+l=4+0=4n+l=4+0=4n+l=4+0=4
  • For 3p3p3p: n+l=3+1=4n+l=3+1=4n+l=3+1=4
  • For 3d3d3d: n+l=3+2=5n+l=3+2=5n+l=3+2=5
  1. Arrange by decreasing energy

Highest (n+l)(n+l)(n+l) means highest energy:

  • 3d3d3d has 555 ⇒\Rightarrow⇒ highest
  • 4s4s4s and 3p3p3p both have 444
    • Between them, higher nnn means higher energy
    • So 4s>3p4s > 3p4s>3p
  • 3s3s3s has 333 ⇒\Rightarrow⇒ lowest

Therefore, 3d>4s>3p>3s3d > 4s > 3p > 3s3d>4s>3p>3s

  1. Map back to letters
  • 3d⇒D3d \Rightarrow D3d⇒D
  • 4s⇒B4s \Rightarrow B4s⇒B
  • 3p⇒C3p \Rightarrow C3p⇒C
  • 3s⇒A3s \Rightarrow A3s⇒A

So the decreasing order is D>B>C>AD > B > C > AD>B>C>A

  1. Check options

This corresponds to Option D.

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