type: error_analysis | subtopic: Common Mistakes

Trap 1: KE Sign in Bohr Model

Wrong: Students assume KE = E_n = −13.6 eV (negative). Correct: KE = −E_n = +13.6 eV. Kinetic energy is ALWAYS positive (½$mv^{2}$ > 0). The total energy is negative (bound state); KE has the opposite sign to total energy.

Trap 2: PE Sign in Bohr Model

Wrong: PE = −2E_n = +27.2 eV (positive). Correct: PE = 2E_n = 2×(−13.6) = −27.2 eV (negative). For Coulomb attractive force: PE = 2E (same sign as E, which is negative). "PE doubles E; KE opposes E."

Trap 3: Spectral Lines Formula

Wrong: N = $n^{2}$ or N = 2n. Correct: N = n(n−1)/2. From n=4: N = 4×3/2 = 6 (not 16 or 8). From n=5: N = 10 (not 25 or 10 by 2n).

Trap 4: Mean Life vs Half-Life

Wrong: τ = t_{1}/{2} or τ = 0.693 × t{1}/{2}. Correct: τ = t{1}/{2}/0.693 = 1.443 × t{1}/{2}. Mean life is GREATER than half-life, not less. If λ = 0.01 $s^{-1}$: t{1}/_{2} = 69.3 s, τ = 100 s.

Trap 5: Balmer Series Region

Wrong: "All spectral lines of hydrogen are in the visible." Correct: ONLY the Balmer series is in the visible region. Lyman = UV, Paschen = IR, Brackett = far IR, Pfund = far IR. The Balmer series also extends into near UV (series limit at 364.6 nm is near UV, not visible).

Trap 6: Beta-Minus vs Beta-Plus Decay

Wrong: Confusing β^{-} (Z+1) with β^{+} (Z−1). Correct: β^{-} decay: Z INCREASES by 1 (neutron → proton). β^{+} decay: Z DECREASES by 1 (proton → neutron). Mnemonic: beta-minus releases an electron (negative charge) and increases Z.

Trap 7: Nuclear Density

Wrong: "Heavier nuclei are denser." Correct: Nuclear density is CONSTANT for ALL nuclei (~$2.3 \times 10^{17}$ kg/$m^{3}$), independent of mass number A. Both mass (∝ A) and volume (∝ A) scale the same way.

Trap 8: Series Limit vs First Line

Wrong: "The longest wavelength in a series = series limit." Correct: Series limit = SHORTEST wavelength (n_{2} → ∞, maximum energy). First line = LONGEST wavelength (smallest energy gap, lowest n_{2}). Mnemonic: "limit" is the extreme end = shortest λ.