Formula Explanation

The maximum number of electrons in any shell is given by 2n², where n is the principal quantum number. For n=2 (the L shell), substitute to get 2×(2)²=2×4=8 electrons. This formula arises from quantum mechanics: each shell has n subshells, each subshell has up to 2 orbitals (from azimuthal quantum number l=0 to n-1), and each orbital holds 2 electrons (Pauli exclusion principle, spin quantum number ms=±1/2).

Step-by-Step Solution

• Identify n=2 as given (principal quantum number defines the shell).
• Compute n² = 4.
• Multiply by 2: 8 electrons maximum.

No options are provided in the query, but common alternatives like 2, 4, 18, or 32 fail because they match other shells (n=1: 2; n=3: 18; n=4: 32) or ignore the formula.

Shell Capacities Table

Why 2n² Determines Electron Capacity

The maximum number of electrons in shell n=2 is a foundational concept in atomic structure, crucial for CSIR NET Life Sciences aspirants studying quantum numbers and electron configurations. Defined by the principal quantum number (n), shells organize electrons around the nucleus, with capacity dictated by the 2n² rule derived from quantum mechanics.

Each shell n supports n subshells (l=0 to n-1), with 2l+1 orbitals per subshell, each holding 2 electrons, yielding 2n². For maximum number of electrons in shell n=2, n=2 gives one s (l=0, 2 electrons) and one p (l=1, 6 electrons) subshell, totaling 8. This explains neon’s stable configuration (1s² 2s² 2p⁶).

CSIR NET Relevance

In competitive exams like CSIR NET, questions test this for electron distribution, valency, and bonding. Misapplying (e.g., assuming 18 for n=2) confuses it with n=3. Practice: n=1 holds 2 (helium), n=2 holds 8 (neon core).

Quick Shell Capacities

• n=1: 2 electrons
• n=2: 8 electrons
• n=3: 18 electrons
• n=4: 32 electrons

Mastering maximum number of electrons in shell n=2 via 2n² ensures exam success in molecular biology and biochemistry topics.