Error 1: Spectral Lines Formula

Wrong: Lines from n = $n^{2}$ (number of orbitals) Wrong: Lines from n = n (number of energy levels) Correct: $\text{Lines} = \frac{n(n-1)}{2}$ Example: From n=5: NOT 25, NOT 5, BUT 10.

Error 2: Quantum Number Validity

Wrong: Assuming l can equal n (e.g., n=2, l=2) Correct: l ranges from 0 to (n−1). For n=2: l = 0 or 1 ONLY. Rule: l < n always.

Error 3: Energy Sign in Bohr Model

Wrong: Taking $\Delta E$ = $E_{2}$ − $E_{1}$ without considering signs Correct: For emission (higher→lower): $\Delta E$ = |E_lower − E_upper| = positive Formula: $\Delta E$ = 13.6$Z^{2}$(1/n_{1}^{2} − 1/n_{2}^{2}) where n_{1} < n_{2}

Error 4: Photoelectric Effect — Intensity vs Frequency

Wrong: Higher intensity increases KE of electrons Correct: Higher intensity = more electrons (not higher KE). KE depends ONLY on frequency. Rule: Frequency determines IF emission occurs and KE; intensity determines HOW MANY electrons.

Error 5: Anomalous Configurations

Wrong: Cr = [Ar] 3$d^{4}$ 4$s^{2}$, Cu = [Ar] 3$d^{9}$ 4$s^{2}$ Correct: Cr = [Ar] 3$d^{5}$ 4$s^{1}$ (half-filled d); Cu = [Ar] 3$d^{10}$ 4$s^{1}$ (full d) Rule: Half-filled and fully-filled d/f subshells are extra stable.

Error 6: Electron Removal Order in Ions

Wrong: Removing 3d electrons before 4s when forming 3d metal cations Correct: 4s electrons are always removed FIRST from transition metals. Example: Fe ([Ar]3$d^{6}$4$s^{2}$) → $Fe^{3+}$ ([Ar]3$d^{5}$): removes 4$s^{2}$ then one 3d.

Error 7: de Broglie and KE

Wrong: λ ∝ 1/KE Correct: λ = h/p = h/√(2mKE) → λ ∝ 1/√(KE) Doubled KE: λ decreases by factor √2, NOT halved.

Error 8: Nodes in Orbitals

Wrong: Node = region of maximum electron density Correct: Node = region where probability of finding electron = ZERO. Formula reminder: Radial nodes = n−l−1 (often confused with n−l or n−1).