type: misconceptions | subtopic: Conceptual Errors
Misconception 1: "Nuclear density increases with mass number"
Reality: Nuclear density is CONSTANT (~ kg/) for all nuclei, from H to U. Because R ∝ A^(1/3), volume ∝ A, and mass ∝ A, density = constant × A/(constant × A) = constant.
Misconception 2: "Heavier elements have larger nuclei"
Partial truth: Heavier elements DO have larger nuclei (R = 1.2 × A^(1/3)), but only in proportion to A^(1/3). U-238 has radius ≈ 7.4 fm; H-1 has radius ≈ 1.2 fm. Ratio = 7.4/1.2 ≈ 6.2, but mass ratio = 238:1.
Misconception 3: "Electrons in the Bohr model radiate energy while orbiting"
Reality: Bohr's first postulate explicitly states electrons do NOT radiate in stationary orbits. Classical physics predicts radiation from accelerating charges, but Bohr's model assumes this doesn't happen in quantized orbits. Radiation occurs ONLY during transitions.
Misconception 4: "Mean life = half-life"
Reality: Mean life τ = 1.443 × t_{1}/{2} > t{1}/{2}. They are different quantities. At t = t{1}/_{2}: 50% remains. At t = τ: 36.8% (= 1/e) remains.
Misconception 5: "The series limit has the longest wavelength"
Reality: Series limit has the SHORTEST wavelength (highest energy). It corresponds to the transition from n=∞ to n_{1}. The FIRST LINE (lowest n_{2}) has the longest wavelength (lowest energy transition).
Misconception 6: "Fe-56 is stable because it has equal protons and neutrons"
Partial: Fe-56 has Z=26, N=30 (not equal). Its stability comes from maximum BE/A (best balance of short-range strong force and Coulomb repulsion), not from N=Z equality.
Misconception 7: "All radiation is dangerous"
Nuance: Medical use of radiation (X-rays, MRI, gamma therapy) is beneficial with controlled doses. Risk depends on type (alpha, beta, gamma), energy, and exposure. Alpha radiation cannot penetrate skin; danger comes from ingestion/inhalation.
Misconception 8: "Higher energy state electrons move faster"
Reality: In Bohr model, v_n ∝ Z/n. Higher n → LOWER velocity. Electrons in inner orbits (smaller n) move faster. An electron in n=1 moves at ~c/137; in n=4 it moves at ~c/548. Higher energy state means less bound (less negative energy), but slower orbital speed.