The maximum number of electrons that can occupy the shell having a principal quantum number of 3 is

Analyze the question: We need the maximum number of electrons in the shell where n = 3 (the M shell).

Concept: The maximum number of electrons in a shell is given by the formula:

Maximum electrons = 2n²

This comes from the fact that each shell n contains n² orbitals, and each orbital holds 2 electrons.

Step-by-step solution:

For n = 3:

• Maximum electrons = 2 × 3² = 2 × 9 = 18

Check by subshells:

• 3s: 1 orbital → 2 electrons
• 3p: 3 orbitals → 6 electrons
• 3d: 5 orbitals → 10 electrons

Total = 2 + 6 + 10 = 18 electrons

Why the other options are wrong:

• A (3): This is just the value of n itself.
• B (9): This is n² (the number of orbitals), not the number of electrons.
• C (10): This is the capacity of the d subshell alone.
• E (32): This is the maximum for n = 4 (2 × 4² = 32).

Exam tip: Remember the pattern 2n²: n=1 → 2, n=2 → 8, n=3 → 18, n=4 → 32. Be careful not to confuse the maximum capacity of a shell with the number of electrons it holds in a particular atom. For example, in the M shell of argon, it holds 8 electrons, but its maximum capacity is 18.