Key Points: Common Errors in Atoms & Nuclei

Error 1: KE Sign Convention Students often write KE = E_n = −13.6 eV (negative). WRONG. KE = −E_n = +13.6 eV (always positive). Kinetic energy ½$mv^{2}$ can never be negative. The total energy is negative; KE has the opposite sign.

Error 2: PE Sign Convention PE = 2E_n. Since E_n < 0, PE = 2×(negative) = negative. Students sometimes incorrectly write PE = −2E_n = positive. PE is always negative for a bound Coulomb system.

Error 3: Spectral Lines Formula N = n(n−1)/2, NOT $n^{2}$ or 2n. From n=4: N = 6 (not 16 or 8). This is the most commonly misremembered formula.

Error 4: Balmer Series Extends Beyond Visible The Balmer series spans 364.6 nm (series limit, near UV) to 656.3 nm (H-α, red). The visible range is approximately 380–780 nm. So the Balmer series limit (364.6 nm) is technically in the near UV. However, the prominent lines (H-α through H-δ) are in the visible. For NEET, Balmer = visible region is the standard answer.

Error 5: Mean Life vs Half-Life τ = t_{1}/{2}/0.693 = 1.443 × t{1}/{2}. Mean life is GREATER than half-life. If asked to find mean life, do NOT simply write t{1}/_{2}.

Error 6: Beta-Plus Decay Direction β^{+} decay (positron emission): Z decreases by 1 (proton converts to neutron). Students confuse with β^{-} (Z increases by 1). Mnemonic: beta-plus emits a positive particle (positron); losing a positive charge means Z goes down.

Error 7: Series Limit = Longest Wavelength Series limit = SHORTEST wavelength (maximum energy, n_{2}→∞). First line = longest wavelength.

Error 8: Nuclear Density Varies with A Nuclear density is CONSTANT for ALL nuclei. It does not depend on A or Z.