Q.State the two major limitations of Rutherford's nuclear model of the atom, explaining briefly why each was a genuine problem for classical physics.

Limitation 1 -- instability. Classical electromagnetic theory requires any accelerating charge to radiate energy continuously. An electron in circular orbit is always accelerating (centripetally), so classically it must continuously lose energy as radiation; as it loses energy its orbit must shrink, so it should spiral into the nucleus in about $10^{-8}\ \text{s}$ (Exercise 3 examines this timescale argument in more depth). This directly contradicts the observed fact that atoms are stable and persist unchanged indefinitely.

Limitation 2 -- the spectral problem. As the electron spirals inward, its orbital radius -- and hence its orbital (and, classically, its radiated) frequency -- would change smoothly and continuously. The emitted radiation should therefore sweep continuously through every frequency, giving a smooth, continuous spectrum. But real atoms, such as hydrogen, are observed to emit or absorb light only at certain sharply defined, discrete wavelengths -- a line spectrum (Section 1.6), not a continuous one.

State each limitation as a clash between a definite classical prediction and a definite experimental fact -- collapse-vs-stability, continuous-vs-discrete.

• Describing only the instability problem and omitting the (equally important, syllabus-tested) spectral problem.
• Vaguely saying the model is "incomplete" without stating what it actually predicted and why that prediction fails.