Consider the following statements: (A) The principal quantum number 'n' is a positive integer with values n = 1, 2, 3,…

🧠 The Quantum Rulebook The four quantum numbers ($n, l, m, s$) act as the universal address for an electron. They follow strict hierarchical rules that limit their possible values.

🗺️ The Statement Verification

• (A): $n$ must be a positive integer ($1, 2, 3...$). Correct.
• (B): FALSE. $l$ ranges from $0$ to $n-1$. It cannot be equal to $n$. A shell with $n=3$ has no $l=3$ (3f doesn't exist).
• (C): For a given $l$, $m$ ranges from $-l$ to $+l$, giving $(2l+1)$ values. Correct.
• (D): Electrons can only have "up" or "down" spin ($pm 1/2$). Correct.
• (E): FALSE. Total orbitals for a given $l$ is $(2l+1)$. For $l=5$, count is $2(5)+1 = 11$, not 9.

Correct set: A, C, D.

⚡ The "l < n" Rule If you ever see $l=n$, it's a quantum crime. The subshell number is always strictly smaller than the floor number.

⚠️ Common Traps Statement B is the most frequent trick. Students often forget the "$n-1$" limit. Always check if $l$ hits the $n$ ceiling!

$\boxed{\text{Answer: (c)}}$