JEE Main · 2023 · Shift-IIeasyATOM-011

Maximum number of electrons that can be accommodated in shell with n = 4 are:

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

Question

Maximum number of electrons that can be accommodated in shell with n=4n = 4 are:

Options
  1. a

    16

  2. b

    32

  3. c

    50

  4. d

    72

Correct Answerb

32

Detailed Solution

🧠 The Shell Capacity Rule A principal quantum number (nn) defines a shell. Within it, we have subshells (ll) where electrons live. Pauli's Exclusion Principle dictates the limit.

🗺️ The Bohr-Stoner Method The total capacity of any shell nn is calculated using: Max Electrons=2n2\text{Max Electrons} = 2n^2 For n=4n = 4: Max Electrons=2×(4)2=2×16=32\text{Max Electrons} = 2 \times (4)^2 = 2 \times 16 = 32

The Subshell Count For n=4n=4, we have four subshells:

  • 4s: 2 electrons
  • 4p: 6 electrons
  • 4d: 10 electrons
  • 4f: 14 electrons Sum =2+6+10+14=32= 2 + 6 + 10 + 14 = 32. It's always faster to remember the 2n22n^2 rule, but counting subshells is a great way to verify!

⚠️ Common Traps Be careful not to confuse "number of orbitals" (n2=16n^2 = 16) with "number of electrons" (2n2=322n^2 = 32). Each orbital houses two electrons (with opposite spins).

Answer: (b)\boxed{\text{Answer: (b)}}

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