3.4Development of Quantum Theory

• Alongside2.6Quadratic Equations

  The maximum electrons in shell n is 2n², and one exercise runs this backward — given a shell holding 32 electrons, find n — which is solved by isolating n² (n² = 16) and taking a square root, discarding the negative root since n must be a positive integer; recognizing that ±4 is not both physically valid is the same discipline the algebra course drills when solving quadratics by the square-root property, though small perfect squares like this one are also guessable without it.

• Alongside5.9Modeling Using Variation

  The de Broglie wavelength λ = h/(mv) is explained explicitly through inverse proportionality — 'de Broglie wavelength is inversely proportional to both particle mass and velocity' — and explaining why a thrown softball has no detectable wavelength depends on recognizing that inverse variation drives λ toward zero as mv grows, a reasoning move that naming as formal variation sharpens without strictly requiring it.

No algebra turns up here. Most of the descriptive sections need none.